A369735 Number of solutions to 1^3*k_1 + 2^3*k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

0, 1, 1, 1, 1, 1, 3, 4, 6, 15, 28, 56, 125, 287, 646, 1540, 3625, 8484, 21167, 51458, 126342, 323126, 811538, 2052501, 5339265, 13751212, 35589866, 94032931, 246791641, 650227636, 1739032299, 4630165425, 12373805281, 33429284691, 90073865814, 243460560324

Offset: 0

Author

Ilya Gutkovskiy, Jan 30 2024

Keywords

• nonn

Crossrefs

Cf. A007576, A063866, A369345, A369437, A369628, A369734.

Programs

Maple

b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(1, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 30 2024

Mathematica

Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, 1], {n, 0, 33}]

Formula

a(n) = [x^1] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).