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A023358
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Number of compositions into sums of cubes.
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21
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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, 150, 187, 232, 286, 351, 430, 527, 649, 802, 993, 1230, 1522, 1880, 2318, 2854, 3514, 4330, 5341, 6594, 8145, 10061, 12423, 15330, 18908, 23316, 28753, 35467, 43762, 54010, 66665, 82281, 101540, 125286, 154566, 190682
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OFFSET
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0,9
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LINKS
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T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 501 terms from T. D. Noe)
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FORMULA
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G.f.: 1 / (1 - Sum_{n>=1} x^(n^3) ). - Joerg Arndt, Mar 30 2014
a(n) ~ c * d^n, where d = 1.2338881403372741887535479..., c = 0.418031200641837887398653... - Vaclav Kotesovec, May 01 2014
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
`if`(n<0, 0, add(a(n-i^3), i=1..iroot(n, 3))))
end:
seq(a(n), n=0..80); # Alois P. Heinz, Sep 08 2014
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MATHEMATICA
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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 *)
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PROG
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(PARI) E=6; N=E^3-1; q='q+O('q^N);
gf=1/(1 - sum(n=1, E, q^(n^3) ) ); \\ test, several similar seqs.
v=Vec(gf) \\ Joerg Arndt, Mar 30 2014
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CROSSREFS
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Sequence in context: A017902 A005710 A291146 * A322855 A322803 A322800
Adjacent sequences: A023355 A023356 A023357 * A023359 A023360 A023361
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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