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Search: a038541 -id:a038541
Displaying 1-10 of 19 results found. page 1 2
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A352550 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5. +10
21
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
LINKS
Table of n, a(n) for n=1..95.
Don Zagier, On the Number of n-Element Modules Over the Ring of Integers in a Quadratic Number Field [Based on email to N. J. A. Sloane, March 18 2022]
PROG
(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)
CROSSREFS
Cf. A038540, A038541, A248107, A352551-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
A038540 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 40. +10
20
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Equivalently, number of modules with n elements over ring Z[sqrt(10)].
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..96.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn,mult
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it)
EXTENSIONS
Edited by M. F. Hasler, Feb 18 2022
Revised by N. J. A. Sloane, Mar 21 2022
STATUS
approved
A352567 a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -19. +10
19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..116.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352566.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 21 2022
STATUS
approved
A352551 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 8. +10
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..96.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
A352561 a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -3. +10
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
COMMENTS
See A352550 for comments and PARI code.
Appears to be the same sequence as A248107.
LINKS
Table of n, a(n) for n=1..94.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 21 2022
STATUS
approved
A352566 a(n) = number of modules with n elements over the ring of integers in the imaginary quadratic field of discriminant -15. +10
1
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; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..112.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 21 2022
STATUS
approved
A352552 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 12. +10
0
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; internal format)
OFFSET
1,4
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..95.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
A352553 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 13. +10
0
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)
OFFSET
1,3
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..116.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
A352554 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 17. +10
0
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; internal format)
OFFSET
1,2
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..150.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
A352555 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 21. +10
0
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)
OFFSET
1,5
COMMENTS
See A352550 for comments and PARI code.
LINKS
Table of n, a(n) for n=1..118.
CROSSREFS
Cf. A038540, A038541, A248107, A352550-A352567.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2022
STATUS
approved
page 1 2

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Last modified August 21 19:22 EDT 2024. Contains 375353 sequences. (Running on oeis4.)