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A340980 Number of ways to write n as an ordered sum of 7 positive cubes.

%I A340980 #9 Feb 02 2021 21:10:25
%S A340980 1,0,0,0,0,0,0,7,0,0,0,0,0,0,21,0,0,0,0,0,0,35,0,0,0,0,7,0,35,0,0,0,0,
%T A340980 42,0,21,0,0,0,0,105,0,7,0,0,0,0,140,0,1,0,0,21,0,105,0,0,0,0,105,0,
%U A340980 42,0,7,0,0,210,0,7,0,42,0,0,210,0,0,0,105,35,0,105,0,0,0,140,140,0,21,0,42
%N A340980 Number of ways to write n as an ordered sum of 7 positive cubes.
%H A340980 Robert Israel, <a href="/A340980/b340980.txt">Table of n, a(n) for n = 7..10000</a>
%H A340980 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340980 G.f.: (Sum_{k>=1} x^(k^3))^7.
%p A340980 b:= proc(n, t) option remember;
%p A340980       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340980       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340980     end:
%p A340980 a:= n-> b(n, 7):
%p A340980 seq(a(n), n=7..96);  # _Alois P. Heinz_, Feb 01 2021
%t A340980 nmax = 96; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y A340980 Cf. A000578, A010057, A025460, A051344, A173676, A280618, A340977, A340978, A340979, A340981, A340982, A340983.
%K A340980 nonn
%O A340980 7,8
%A A340980 _Ilya Gutkovskiy_, Feb 01 2021