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A025430
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Number of partitions of n into 6 nonzero squares.
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18
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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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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^6] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(n-i-j-k-l-m). - 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), 6):
seq(a(n), n=0..120); # Alois P. Heinz, May 30 2014
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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];
a /@ Range[0, 120] (* Jean-François Alcover, Nov 06 2020, after Alois P. Heinz *)
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CROSSREFS
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Column k=6 of A243148.
Sequence in context: A354579 A306261 A329722 * A256972 A352999 A280747
Adjacent sequences: A025427 A025428 A025429 * A025431 A025432 A025433
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KEYWORD
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nonn,easy
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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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