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A023358 Number of compositions into sums of cubes.

%I A023358 #28 Oct 27 2023 19:24:03
%S A023358 1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,11,14,18,23,29,36,44,53,64,78,96,120,
%T A023358 150,187,232,286,351,430,527,649,802,993,1230,1522,1880,2318,2854,
%U A023358 3514,4330,5341,6594,8145,10061,12423,15330,18908,23316,28753,35467,43762,54010,66665,82281,101540,125286,154566,190682
%N A023358 Number of compositions into sums of cubes.
%H A023358 Alois P. Heinz, <a href="/A023358/b023358.txt">Table of n, a(n) for n = 0..1000</a> (first 501 terms from T. D. Noe)
%F A023358 G.f.: 1 / (1 - Sum_{n>=1} x^(n^3) ). - _Joerg Arndt_, Mar 30 2014
%F A023358 a(n) ~ c * d^n, where d = 1.2338881403372741887535479..., c = 0.418031200641837887398653... - _Vaclav Kotesovec_, May 01 2014
%p A023358 a:= proc(n) option remember; `if`(n=0, 1,
%p A023358       `if`(n<0, 0, add(a(n-i^3), i=1..iroot(n, 3))))
%p A023358     end:
%p A023358 seq(a(n), n=0..80);  # _Alois P. Heinz_, Sep 08 2014
%t A023358 a[n_] := a[n] = If[n==0, 1, If[n<0, 0, Sum[a[n-i^3], {i, 1, Floor[n^(1/3)]}]]]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Apr 08 2015, after _Alois P. Heinz_ *)
%o A023358 (PARI) E=6; N=E^3-1; q='q+O('q^N);
%o A023358 gf=1/(1 - sum(n=1,E, q^(n^3) ) );  \\ test, several similar seqs.
%o A023358 v=Vec(gf) \\ _Joerg Arndt_, Mar 30 2014
%K A023358 nonn
%O A023358 0,9
%A A023358 _David W. Wilson_