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A340982 Number of ways to write n as an ordered sum of 9 positive cubes.

%I A340982 #9 Feb 02 2021 20:05:12
%S A340982 1,0,0,0,0,0,0,9,0,0,0,0,0,0,36,0,0,0,0,0,0,84,0,0,0,0,9,0,126,0,0,0,
%T A340982 0,72,0,126,0,0,0,0,252,0,84,0,0,0,0,504,0,36,0,0,36,0,630,0,9,0,0,
%U A340982 252,0,504,0,10,0,0,756,0,252,0,72,0,0,1260,0,72,0,252,84,0,1260,0,9,0,504,504
%N A340982 Number of ways to write n as an ordered sum of 9 positive cubes.
%H A340982 Robert Israel, <a href="/A340982/b340982.txt">Table of n, a(n) for n = 9..10000</a>
%H A340982 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340982 G.f.: (Sum_{k>=1} x^(k^3))^9.
%p A340982 b:= proc(n, t) option remember;
%p A340982       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340982       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340982     end:
%p A340982 a:= n-> b(n, 9):
%p A340982 seq(a(n), n=9..94);  # _Alois P. Heinz_, Feb 01 2021
%t A340982 nmax = 94; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A340982 Cf. A000578, A010057, A025462, A051344, A173682, A280618, A340977, A340978, A340979, A340980, A340981, A340983.
%K A340982 nonn
%O A340982 9,8
%A A340982 _Ilya Gutkovskiy_, Feb 01 2021