A340977 - OEIS

%I #9 Feb 02 2021 21:09:51

%S 1,0,0,0,0,0,0,4,0,0,0,0,0,0,6,0,0,0,0,0,0,4,0,0,0,0,4,0,1,0,0,0,0,12,

%T 0,0,0,0,0,0,12,0,0,0,0,0,0,4,0,0,0,0,6,0,0,0,0,0,0,12,0,0,0,4,0,0,6,

%U 0,0,0,12,0,0,0,0,0,0,12,4,0,0,0,0,0,4,4,0,0,0,12,0,0,0,0,0,0,24

%N Number of ways to write n as an ordered sum of 4 positive cubes.

%H Robert Israel, <a href="/A340977/b340977.txt">Table of n, a(n) for n = 4..10000</a>

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

%F G.f.: (Sum_{k>=1} x^(k^3))^4.

%p b:= proc(n, t) option remember;

%p       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->

%p       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))

%p     end:

%p a:= n-> b(n, 4):

%p seq(a(n), n=4..100);  # _Alois P. Heinz_, Feb 01 2021

%t nmax = 100; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

%Y Cf. A000578, A010057, A025457, A051344, A173678, A280618, A340978, A340979, A340980, A340981, A340982, A340983.

%K nonn

%O 4,8

%A _Ilya Gutkovskiy_, Feb 01 2021