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A332796
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Number of compositions of n^2 into parts >= n.
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5
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1, 1, 2, 6, 26, 140, 882, 6349, 51284, 457704, 4459940, 47019819, 532485538, 6438774524, 82710138994, 1123798871990, 16090426592488, 241979954659728, 3811335657375786, 62712512310820402, 1075527196672980525, 19186234784992217621, 355349469934379290700
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(0) = 1: (), the empty composition.
a(1) = 1: 1.
a(2) = 2: 22, 4.
a(3) = 6: 333, 36, 63, 45, 54, 9.
a(4) = 26: 4444, 556, 565, 655, 466, 646, 664, 457, 475, 547, 574, 745, 754, 448, 484, 844, 88, 79, 97, 6(10), (10)6, 5(11), (11)5, 4(12), (12)4, (16).
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MAPLE
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b:= proc(n, k) option remember; `if`(n=0, 1,
add(b(n-j, k), j=k..n))
end:
a:= n-> b(n^2, n):
seq(a(n), n=0..23);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k], {j, k, n}]];
a[n_] := b[n^2, 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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