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A240944
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Number of compositions of n into square parts k^2 where there are k sorts of part k^2.
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4
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1, 1, 1, 1, 3, 5, 7, 9, 15, 28, 45, 66, 99, 164, 269, 422, 651, 1028, 1654, 2637, 4149, 6522, 10350, 16467, 26091, 41205, 65174, 103339, 163833, 259361, 410376, 649827, 1029543, 1630725, 2581848, 4087797, 6473832, 10253370, 16237375, 25711316, 40714953, 64478427, 102111230, 161701086, 256062990, 405499697, 642156651
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: 1/(1 - sum(k>=1, k * x^(k^2)) ).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, `if`(n<0, 0,
add(k*a(n-k^2), k=1..isqrt(n))))
end:
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MATHEMATICA
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a[n_] := a[n] = If[n == 0, 1, If[n<0, 0, Sum[k*a[n-k^2], {k, Sqrt[n]}]]];
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(1/(1 - sum(k=1, 1+sqrtint(N), k * x^(k^2))) )
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CROSSREFS
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Cf. A006456 (compositions into squares).
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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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