cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A290247 Number of compositions (ordered partitions) of n^3 into cubes.

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%I A290247 #19 Aug 12 2017 09:30:40
%S A290247 1,1,2,120,290250,107320441096,21715974961480054078,
%T A290247 8487986089807555456140271121440,
%U A290247 22615863021403796876556069287242400147213424924,1449638083412288206280215383952017948209203861522683138464747658192
%N A290247 Number of compositions (ordered partitions) of n^3 into cubes.
%H A290247 Alois P. Heinz, <a href="/A290247/b290247.txt">Table of n, a(n) for n = 0..22</a>
%H A290247 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A290247 a(n) = [x^(n^3)] 1/(1 - Sum_{k>=1} x^(k^3)).
%F A290247 a(n) = A023358(A000578(n)).
%e A290247 a(2) = 2 because 2^3 = 8 and we have [8], [1, 1, 1, 1, 1, 1, 1, 1].
%p A290247 b:= proc(n) option remember; local i; if n=0 then 1
%p A290247       else 0; for i while i^3<=n do %+b(n-i^3) od fi
%p A290247     end:
%p A290247 a:= n-> b(n^3):
%p A290247 seq(a(n), n=0..10);  # _Alois P. Heinz_, Aug 12 2017
%t A290247 Table[SeriesCoefficient[1/(1 - Sum[x^k^3, {k, 1, n}]), {x, 0, n^3}], {n, 0, 9}]
%Y A290247 Cf. A000578, A023358, A030272, A224366, A259792.
%K A290247 nonn
%O A290247 0,3
%A A290247 _Ilya Gutkovskiy_, Jul 24 2017