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 A025430 Number of partitions of n into 6 nonzero squares. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,22 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA 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 MAPLE 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 MATHEMATICA 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 *) CROSSREFS Column k=6 of A243148. Sequence in context: A354579 A306261 A329722 * A256972 A352999 A280747 Adjacent sequences: A025427 A025428 A025429 * A025431 A025432 A025433 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 7 17:11 EST 2023. Contains 360128 sequences. (Running on oeis4.)