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A340977 Number of ways to write n as an ordered sum of 4 positive cubes.

%I A340977 #9 Feb 02 2021 21:09:51
%S A340977 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 A340977 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 A340977 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 A340977 Number of ways to write n as an ordered sum of 4 positive cubes.
%H A340977 Robert Israel, <a href="/A340977/b340977.txt">Table of n, a(n) for n = 4..10000</a>
%H A340977 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340977 G.f.: (Sum_{k>=1} x^(k^3))^4.
%p A340977 b:= proc(n, t) option remember;
%p A340977       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340977       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340977     end:
%p A340977 a:= n-> b(n, 4):
%p A340977 seq(a(n), n=4..100);  # _Alois P. Heinz_, Feb 01 2021
%t A340977 nmax = 100; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A340977 Cf. A000578, A010057, A025457, A051344, A173678, A280618, A340978, A340979, A340980, A340981, A340982, A340983.
%K A340977 nonn
%O A340977 4,8
%A A340977 _Ilya Gutkovskiy_, Feb 01 2021