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A025460
Number of partitions of n into 7 positive cubes.
3
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, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0
OFFSET
0,132
COMMENTS
The first term > 1 is a(131) = 2. - Michel Marcus, Apr 23 2019
FORMULA
a(n) = [x^n y^7] 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), 7):
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, 7];
a /@ Range[0, 120] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A320841.
Sequence in context: A037823 A293162 A115790 * A374222 A169673 A101605
KEYWORD
nonn
EXTENSIONS
Second offset from Michel Marcus, Apr 23 2019
STATUS
approved