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A025462 Number of partitions of n into 9 positive cubes. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,73

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..65536

Index entries for sequences related to sums of cubes

FORMULA

a(n) = [x^n y^9] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),

      `if`(i<1 or t<1, 0, b(n, i-1, t)+

      `if`(i^3>n, 0, b(n-i^3, i, t-1))))

    end:

a:= n-> b(n, iroot(n, 3), 9):

seq(a(n), n=0..120);  # Alois P. Heinz, Dec 21 2018

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^3 > n, 0, b[n - i^3, i, t - 1]]]];

a[n_] := b[n, n^(1/3) // Floor, 9];

a /@ Range[0, 120] (* Jean-Fran├žois Alcover, Dec 04 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000578 (cubes).

Column k=9 of A320841.

Sequence in context: A307505 A035162 A121454 * A024879 A024316 A345375

Adjacent sequences:  A025459 A025460 A025461 * A025463 A025464 A025465

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 24 05:19 EDT 2021. Contains 348217 sequences. (Running on oeis4.)