Search: a038541 -id:a038541
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A352550
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5.
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+10
21
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1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2
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OFFSET
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1,11
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LINKS
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PROG
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(PARI) \\ Don Zagier, Mar 18 2022
PZ(D, m=20) = Z=dirmul(vector(m, n, 1), vD=vector(m, n, kronecker(D, n))); v=Z; \
for(j=2, log(m)/log(2), V=v*0; for(k=1, m^(1/j), V[k^j]=Z[k]); v=dirmul(v, V)); v
PZ(5, 100)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A038540
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 40.
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+10
20
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1, 1, 2, 2, 1, 2, 0, 3, 5, 1, 0, 4, 2, 0, 2, 5, 0, 5, 0, 2, 0, 0, 0, 6, 2, 2, 10, 0, 0, 2, 2, 7, 0, 0, 0, 10, 2, 0, 4, 3, 2, 0, 2, 0, 5, 0, 0, 10, 1, 2, 0, 4, 2, 10, 0, 0, 0, 0, 0, 4, 0, 2, 0, 11, 2, 0, 2, 0, 0, 0, 2, 15, 0, 2, 4, 0, 0, 4, 2, 5, 20, 2, 2, 0, 0, 2, 0, 0, 2, 5, 0, 0, 4, 0, 0, 14
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OFFSET
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1,3
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COMMENTS
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Equivalently, number of modules with n elements over ring Z[sqrt(10)].
See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it)
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EXTENSIONS
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STATUS
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approved
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A352567
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a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -19.
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+10
19
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1, 0, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 3, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 4, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0
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OFFSET
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1,5
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352551
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 8.
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+10
1
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1, 1, 0, 2, 0, 0, 2, 3, 1, 0, 0, 0, 0, 2, 0, 5, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 4, 0, 0, 2, 7, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 5, 1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 11, 0, 0, 0, 4, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0
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OFFSET
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1,4
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352561
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a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -3.
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+10
1
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1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 3, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 5, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 3, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0
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OFFSET
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1,7
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COMMENTS
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See A352550 for comments and PARI code.
Appears to be the same sequence as A248107.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352566
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a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -15.
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+10
1
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1, 2, 1, 5, 1, 2, 0, 10, 2, 2, 0, 5, 0, 0, 1, 20, 2, 4, 2, 5, 0, 0, 2, 10, 2, 0, 3, 0, 0, 2, 2, 36, 0, 4, 0, 10, 0, 4, 0, 10, 0, 0, 0, 0, 2, 4, 2, 20, 1, 4, 2, 0, 2, 6, 0, 0, 2, 0, 0, 5, 2, 4, 0, 65, 0, 0, 0, 10, 2, 0, 0, 20, 0, 0, 2, 10, 0, 0, 2, 20, 5, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 10, 2, 4, 2, 36, 0, 2, 0, 10, 0, 4, 0, 0, 0, 4, 2, 15, 2, 0, 0, 0
(list;
graph;
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listen;
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OFFSET
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1,2
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352552
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 12.
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+10
0
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1, 1, 1, 2, 0, 1, 0, 3, 2, 0, 2, 2, 2, 0, 0, 5, 0, 2, 0, 0, 0, 2, 2, 3, 1, 2, 3, 0, 0, 0, 0, 7, 2, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 5, 1, 1, 0, 4, 0, 3, 0, 0, 0, 0, 2, 0, 2, 0, 0, 11, 0, 2, 0, 0, 2, 0, 2, 6, 2, 2, 1, 0, 0, 2, 0, 0, 5, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0
(list;
graph;
refs;
listen;
history;
text;
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OFFSET
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1,4
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352553
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 13.
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+10
0
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1, 0, 2, 1, 0, 0, 0, 0, 5, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 10, 0, 2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 1, 0, 4, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 20, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 10, 0, 0, 0, 0, 2, 0, 0, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352554
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 17.
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+10
0
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1, 2, 0, 5, 0, 0, 0, 10, 1, 0, 0, 0, 2, 0, 0, 20, 1, 2, 2, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 36, 0, 2, 0, 5, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 10, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 65, 0, 0, 2, 5, 0, 0, 0, 10, 0, 0, 0, 10, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 5, 2, 0, 2, 20, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 1, 0, 0, 0, 0, 0, 2, 110, 0, 0, 0, 0, 0, 4, 0, 10, 2, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 2, 0
(list;
graph;
refs;
listen;
history;
text;
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OFFSET
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1,2
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A352555
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a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 21.
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+10
0
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1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 5, 0, 3, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 4, 5, 0, 2, 1, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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See A352550 for comments and PARI code.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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