OFFSET
0,5
COMMENTS
All terms are odd.
a(n) is the number of solutions to 0 = Sum_{i=1..n} c_i * i*(i+1)/2 with c_i in {-1,0,1}.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ sqrt(5) * 3^(n + 1/2) / (sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Jan 22 2024
MAPLE
b:= proc(n, i) option remember; `if`(n>i*(i+1)*(i+2)/6, 0, `if`(i=0, 1,
b(n, i-1)+b(n+i*(i+1)/2, i-1)+b(abs(n-i*(i+1)/2), i-1)))
end:
a:= n-> b(0, n):
seq(a(n), n=0..33); # Alois P. Heinz, Jan 21 2024
MATHEMATICA
Table[Coefficient[Product[x^(k (k + 1)/2) + 1 + 1/x^(k (k + 1)/2), {k, 1, n}], x, 0], {n, 0, 31}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 20 2024
STATUS
approved