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A025431
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Number of partitions of n into 7 nonzero squares.
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18
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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, 3, 1, 2, 3, 1, 1, 4, 2, 3, 4, 1, 4, 3, 1, 5, 4, 3, 4, 4, 4, 3, 4, 4, 5, 7, 3, 5, 7, 3, 5, 8, 4, 7, 7, 4, 8, 6, 3, 9, 10, 6, 8, 8, 7, 7, 8, 8, 9, 11, 7, 9, 12, 6, 8, 15, 8, 12, 12, 7, 15, 10, 8, 16, 13, 11, 13, 13, 12, 11
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OFFSET
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0,23
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for sequences related to sums of squares
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FORMULA
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a(n) = [x^n y^7] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019
a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) A010052(n-i-j-k-l-m-o). - 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), 7):
seq(a(n), n=0..120); # Alois P. Heinz, May 30 2014
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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, 7];
Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)
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CROSSREFS
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Column k=7 of A243148.
Sequence in context: A340101 A049847 A255274 * A161070 A161109 A161044
Adjacent sequences: A025428 A025429 A025430 * A025432 A025433 A025434
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KEYWORD
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nonn,look
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AUTHOR
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David W. Wilson
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STATUS
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approved
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