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A339421 Number of compositions (ordered partitions) of n into an odd number of cubes.

%I A339421 #9 Dec 03 2020 18:36:37
%S A339421 0,1,0,1,0,1,0,1,1,1,3,1,5,1,7,1,9,4,11,11,13,22,15,37,18,56,29,80,56,
%T A339421 109,107,142,190,184,313,255,490,391,731,644,1045,1082,1458,1792,2044,
%U A339421 2895,2957,4531,4463,6863,6972,10126,11090,14739,17691,21484,27954,31741
%N A339421 Number of compositions (ordered partitions) of n into an odd number of cubes.
%H A339421 Alois P. Heinz, <a href="/A339421/b339421.txt">Table of n, a(n) for n = 0..5000</a>
%H A339421 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A339421 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A339421 G.f.: (1/2) * (1 / (1 - Sum_{k>=1} x^(k^3)) - 1 / Sum_{k>=0} x^(k^3)).
%F A339421 a(n) = (A023358(n) - A323633(n)) / 2.
%F A339421 a(n) = -Sum_{k=0..n-1} A023358(k) * A323633(n-k).
%e A339421 a(10) = 3 because we have [8, 1, 1], [1, 8, 1] and [1, 1, 8].
%p A339421 b:= proc(n, t) option remember; local r, f, g;
%p A339421       if n=0 then t else r, f, g:=$0..2; while f<=n
%p A339421       do r, f, g:= r+b(n-f, 1-t), f+3*g*(g-1)+1, g+1 od; r fi
%p A339421     end:
%p A339421 a:= n-> b(n, 0):
%p A339421 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 03 2020
%t A339421 nmax = 57; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]) - 1/Sum[x^(k^3), {k, 0, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]
%Y A339421 Cf. A000578, A023358, A166444, A323633, A339369, A339419, A339420.
%K A339421 nonn
%O A339421 0,11
%A A339421 _Ilya Gutkovskiy_, Dec 03 2020