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A340979 Number of ways to write n as an ordered sum of 6 positive cubes.

%I A340979 #9 Feb 02 2021 21:09:24
%S A340979 1,0,0,0,0,0,0,6,0,0,0,0,0,0,15,0,0,0,0,0,0,20,0,0,0,0,6,0,15,0,0,0,0,
%T A340979 30,0,6,0,0,0,0,60,0,1,0,0,0,0,60,0,0,0,0,15,0,30,0,0,0,0,60,0,6,0,6,
%U A340979 0,0,90,0,0,0,30,0,0,60,0,0,0,60,20,0,15,0,0,0,60,60,0,0,0,30,0,30,60
%N A340979 Number of ways to write n as an ordered sum of 6 positive cubes.
%H A340979 Robert Israel, <a href="/A340979/b340979.txt">Table of n, a(n) for n = 6..10000</a>
%H A340979 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340979 G.f.: (Sum_{k>=1} x^(k^3))^6.
%p A340979 b:= proc(n, t) option remember;
%p A340979       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340979       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340979     end:
%p A340979 a:= n-> b(n, 6):
%p A340979 seq(a(n), n=6..98);  # _Alois P. Heinz_, Feb 01 2021
%t A340979 nmax = 98; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^6, {x, 0, nmax}], x] // Drop[#, 6] &
%Y A340979 Cf. A000578, A010057, A025459, A051344, A173680, A280618, A340977, A340978, A340980, A340981, A340982, A340983.
%K A340979 nonn
%O A340979 6,8
%A A340979 _Ilya Gutkovskiy_, Feb 01 2021