%I #23 Jan 09 2023 07:41:13

%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,

%T 1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,

%U 0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1

%N Number of partitions of n into 8 positive cubes.

%H Alois P. Heinz, <a href="/A025461/b025461.txt">Table of n, a(n) for n = 0..65536</a>

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

%F a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 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^3>n, 0, b(n-i^3, i, t-1))))

%p end:

%p a:= n-> b(n, iroot(n, 3), 8):

%p seq(a(n), n=0..120); # _Alois P. Heinz_, Dec 21 2018

%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^3 > n, 0, b[n - i^3, i, t - 1]]]];

%t a[n_] := b[n, n^(1/3) // Floor, 8];

%t a /@ Range[0, 120] (* _Jean-François Alcover_, Nov 23 2020, after _Alois P. Heinz_ *)

%Y Column k=8 of A320841.

%K nonn

%O 0,133

%A _David W. Wilson_

%E Second offset 132 from _Michel Marcus_, Apr 23 2019