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A025431 Number of partitions of n into 7 nonzero squares. 18

%I #24 Aug 19 2020 15:45:22

%S 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,

%T 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,

%U 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

%N Number of partitions of n into 7 nonzero squares.

%H Alois P. Heinz, <a href="/A025431/b025431.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F a(n) = [x^n y^7] Product_{k>=1} 1/(1 - y*x^(k^2)). - _Ilya Gutkovskiy_, Apr 19 2019

%F 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

%p b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),

%p `if`(i<1 or t<1, 0, b(n, i-1, t)+

%p `if`(i^2>n, 0, b(n-i^2, i, t-1))))

%p end:

%p a:= n-> b(n, isqrt(n), 7):

%p seq(a(n), n=0..120); # _Alois P. Heinz_, May 30 2014

%t 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]]]];

%t a[n_] := b[n, Sqrt[n] // Floor, 7];

%t Table[a[n], {n, 0, 120}] (* _Jean-François Alcover_, Apr 30 2018, after _Alois P. Heinz_ *)

%Y Column k=7 of A243148.

%K nonn,look

%O 0,23

%A _David W. Wilson_

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)