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A025430 Number of partitions of n into 6 nonzero squares. 16
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

Index entries for sequences related to sums of squares

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-Fran├žois Alcover, Feb 19 2016 *)

CROSSREFS

Column k=6 of A243148.

Sequence in context: A322480 A251683 A306261 * A256972 A280747 A110955

Adjacent sequences:  A025427 A025428 A025429 * A025431 A025432 A025433

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified June 17 05:19 EDT 2019. Contains 324183 sequences. (Running on oeis4.)