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A369704
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Number of pairs (p,q) of partitions of n such that the set of parts in q is a subset of the set of parts in p.
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3
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1, 1, 2, 4, 8, 13, 28, 43, 84, 137, 243, 372, 684, 1010, 1702, 2620, 4256, 6276, 10134, 14740, 23094, 33742, 51139, 73550, 111303, 158140, 233006, 331099, 481324, 674778, 973928, 1353504, 1925734, 2668263, 3748636, 5153887, 7201684, 9820055, 13572468, 18445878
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 13: (11111, 11111), (2111, 11111), (2111, 2111), (2111, 221), (221, 11111), (221, 2111), (221, 221), (311, 11111), (311, 311), (32, 32), (41, 11111), (41, 41), (5, 5).
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MAPLE
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b:= proc(n, m, i) option remember; `if`(n=0,
`if`(m=0, 1, 0), `if`(i<1, 0, b(n, m, i-1)+add(
add(b(n-i*j, m-i*h, i-1), h=0..m/i), j=1..n/i)))
end:
a:= n-> b(n$3):
seq(a(n), n=0..42);
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MATHEMATICA
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b[n_, m_, i_] := b[n, m, i] = If[n == 0, If[m == 0, 1, 0], If[i < 1, 0, b[n, m, i - 1] + Sum[Sum[b[n - i*j, m - i*h, i - 1], {h, 0, m/i}], { j, 1, n/i}]]];
a[n_] := b[n, n, n];
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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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