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A369910
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Number of pairs (p,q) of partitions of n such that the set of parts in q is a proper subset of the set of parts in p.
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3
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0, 0, 0, 1, 3, 4, 15, 20, 52, 83, 163, 246, 501, 727, 1295, 1994, 3375, 4969, 8267, 12036, 19287, 28270, 43511, 62799, 96364, 137358, 204388, 291607, 427446, 601257, 874088, 1218524, 1743989, 2424096, 3422084, 4718626, 6622937, 9053800, 12559895, 17112883
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OFFSET
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0,5
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LINKS
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EXAMPLE
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a(5) = 4: (2111, 11111), (221, 11111), (311, 11111), (41, 11111).
a(6) = 15: (21111, 111111), (21111, 222), (2211, 111111), (2211, 222), (3111, 111111), (321, 111111), (321, 21111), (321, 2211), (321, 222), (321, 3111), (3111, 33), (321, 33), (411, 111111), (42, 222), (51, 111111).
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MAPLE
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b:= proc(n, m, i, t) option remember; `if`(n=0,
`if`(t and m=0, 1, 0), `if`(i<1, 0, b(n, m, i-1, t)+add(
add(b(n-i*j, m-i*h, i-1, h=0 or t), h=0..m/i), j=1..n/i)))
end:
a:= n-> b(n$3, false):
seq(a(n), n=0..42);
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MATHEMATICA
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b[n_, m_, i_, t_] := b[n, m, i, t] = If[n == 0,
If[t && m == 0, 1, 0], If[i < 1, 0, b[n, m, i-1, t] +
Sum[Sum[b[n-i*j, m-i*h, i-1, h == 0 || t], {h, 0, m/i}], {j, 1, n/i}]]];
a[n_] := b[n, n, n, False];
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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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