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A340978 Number of ways to write n as an ordered sum of 5 positive cubes.

%I A340978 #9 Feb 02 2021 21:10:11
%S A340978 1,0,0,0,0,0,0,5,0,0,0,0,0,0,10,0,0,0,0,0,0,10,0,0,0,0,5,0,5,0,0,0,0,
%T A340978 20,0,1,0,0,0,0,30,0,0,0,0,0,0,20,0,0,0,0,10,0,5,0,0,0,0,30,0,0,0,5,0,
%U A340978 0,30,0,0,0,20,0,0,10,0,0,0,30,10,0,0,0,0,0,20,20,0,0,0,20,0,5,10
%N A340978 Number of ways to write n as an ordered sum of 5 positive cubes.
%H A340978 Robert Israel, <a href="/A340978/b340978.txt">Table of n, a(n) for n = 5..10000</a>
%H A340978 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340978 G.f.: (Sum_{k>=1} x^(k^3))^5.
%p A340978 b:= proc(n, t) option remember;
%p A340978       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340978       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340978     end:
%p A340978 a:= n-> b(n, 5):
%p A340978 seq(a(n), n=5..97);  # _Alois P. Heinz_, Feb 01 2021
%t A340978 nmax = 97; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A340978 Cf. A000578, A010057, A025458, A051344, A173679, A280618, A340977, A340979, A340980, A340981, A340982, A340983.
%K A340978 nonn
%O A340978 5,8
%A A340978 _Ilya Gutkovskiy_, Feb 01 2021