Search: id:a025430
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A025430
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Number of partitions of n into 6 nonzero squares.
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+0
19
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0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 4, 1, 3, 3, 1, 4, 2, 1, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 6, 3, 4, 6, 2, 3, 7, 3, 6, 5, 2, 7, 5, 3, 7, 7, 5, 6, 6, 5, 5, 6, 6, 7, 9, 5, 6, 10, 4, 6, 11, 5, 10, 8, 6, 11, 7, 5, 11, 10, 8, 10, 8, 8, 8, 9, 10, 11, 13
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OFFSET
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0,22
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LINKS
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FORMULA
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a(n) = [x^n y^6] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
`if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(i^2>n, 0, b(n-i^2, i, t-1))))
end:
a:= n-> b(n, isqrt(n), 6):
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MATHEMATICA
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a[n_] := Count[PowersRepresentations[n, 6, 2], r_ /; FreeQ[r, 0]]; Array[a, 120, 0] (* Jean-François Alcover, Feb 19 2016 *)
b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^2 > n, 0, b[n - i^2, i, t - 1]]]];
a[n_] := b[n, Sqrt[n] // Floor, 6];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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