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A025434
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Number of partitions of n into 10 nonzero squares.
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6
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0, 0, 0, 0, 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, 2, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 4, 4, 2, 5, 4, 2, 5, 6, 4, 5, 6, 4, 5, 6, 5, 7, 9, 5, 7, 10, 5, 7, 11, 6, 11, 10, 6, 12, 10, 7, 13, 14, 10, 12, 14, 11, 12, 14, 12, 16, 19, 12, 16, 19, 12, 16, 22, 15, 21, 21, 15
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OFFSET
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0,26
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LINKS
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FORMULA
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a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019
a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) * A010052(p) * A010052(q) *A010052(r) * A010052(n-i-j-k-l-m-o-p-q-r). - Wesley Ivan Hurt, 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), 10):
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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, b[n, i - 1, t] + If[i^2 > n, 0, b[n - i^2, i, t - 1]]]];
a[n_] := b[n, Sqrt[n] // Floor, 10];
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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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