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A039901
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Number of partitions satisfying 0 < cn(1,5) + cn(2,5) + cn(3,5) and 0 < cn(4,5) + cn(2,5) + cn(3,5).
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1
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0, 0, 1, 2, 3, 5, 8, 12, 18, 25, 37, 49, 68, 91, 123, 165, 215, 278, 362, 465, 603, 760, 962, 1209, 1524, 1911, 2374, 2934, 3629, 4471, 5514, 6728, 8208, 9982, 12139, 14720, 17772, 21390, 25732, 30889, 37049, 44231, 52749, 62782, 74671, 88640
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OFFSET
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0,4
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COMMENTS
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For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: o < 1 + 2 + 3 and o < 4 + 2 + 3 (OMAABBp).
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LINKS
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MAPLE
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b:= proc(n, i, t, s) option remember; `if`(n=0, t*s,
`if`(i<1, 0, b(n, i-1, t, s)+ `if`(i>n, 0,
b(n-i, i, `if`(irem(i, 5) in {0, 4}, t, 1),
`if`(irem(i, 5) in {0, 1}, s, 1)))))
end:
a:= n-> b(n$2, 0$2):
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MATHEMATICA
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b[n_, i_, t_, s_] := b[n, i, t, s] = If[n == 0, t*s, If[i<1, 0, b[n, i-1, t, s] + If[i>n, 0, b[n-i, i, If[MemberQ[{0, 4}, Mod[i, 5]], t, 1], If[MemberQ[{0, 1}, Mod[i, 5]], s, 1]]]]]; a[n_] := b[n, n, 0, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 12 2015, after Alois P. Heinz *)
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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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