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A025442
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Number of partitions of n into 3 distinct nonzero squares.
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20
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 2, 1, 1
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OFFSET
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0,63
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LINKS
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FORMULA
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a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^(k^2)). - Ilya Gutkovskiy, Apr 22 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, `if`(i=1, 0, b(n, i-1, t))+
`if`(i^2>n, 0, b(n-i^2, i-1, t-1))))
end:
a:= n-> b(n, isqrt(n), 3):
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1 || t<1, 0, If[i==1, 0, b[n, i-1, t]] + If[i^2 > n, 0, b[n-i^2, i-1, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 3]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Oct 10 2015, after Alois P. Heinz *)
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PROG
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(PARI) A025442(n)={sum(x=1, sqrtint(n\3), sum(y=x+1, sqrtint((n-1-x^2)\2), issquare(n-x^2-y^2)))} \\ - M. F. Hasler, Feb 03 2013
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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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