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A340981 Number of ways to write n as an ordered sum of 8 positive cubes.

%I A340981 #11 Feb 02 2021 20:04:45
%S A340981 1,0,0,0,0,0,0,8,0,0,0,0,0,0,28,0,0,0,0,0,0,56,0,0,0,0,8,0,70,0,0,0,0,
%T A340981 56,0,56,0,0,0,0,168,0,28,0,0,0,0,280,0,8,0,0,28,0,280,0,1,0,0,168,0,
%U A340981 168,0,8,0,0,420,0,56,0,56,0,0,560,0,8,0,168,56,0,420,0,0,0,280,280,0,168
%N A340981 Number of ways to write n as an ordered sum of 8 positive cubes.
%H A340981 Robert Israel, <a href="/A340981/b340981.txt">Table of n, a(n) for n = 8..10000</a>
%H A340981 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340981 G.f.: (Sum_{k>=1} x^(k^3))^8.
%p A340981 b:= proc(n, t) option remember;
%p A340981       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340981       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340981     end:
%p A340981 a:= n-> b(n, 8):
%p A340981 seq(a(n), n=8..95);  # _Alois P. Heinz_, Feb 01 2021
%t A340981 nmax = 95; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
%Y A340981 Cf. A000578, A010057, A025461, A051344, A173681, A280618, A340977, A340978, A340979, A340980, A340982, A340983.
%K A340981 nonn,look
%O A340981 8,8
%A A340981 _Ilya Gutkovskiy_, Feb 01 2021