OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3313
FORMULA
G.f.: Sum_{k>=1} x^(k^2)*(1-x)^2/(1-2*x)^2.
a(n) ~ c * 2^n * n, where c = (EllipticTheta[3, 0, 1/2] - 1)/8 = 0.1411171034014846448336823185681189155765645674... - Vaclav Kotesovec, Aug 18 2019, updated Mar 17 2024
EXAMPLE
a(4) = 13: (1)(1)(1)(1), (1)(1)2, (1)2(1), 2(1)(1), 22, (1)3, 3(1), (4).
MAPLE
a:= proc(n) option remember; add(a(n-j)+
`if`(issqr(j), ceil(2^(n-j-1)), 0), j=1..n)
end:
seq(a(n), n=0..33);
MATHEMATICA
CoefficientList[Series[(EllipticTheta[3, 0, x]-1)*(1-x)^2/(2*(1-2*x)^2), {x, 0, 30}], x] (* Vaclav Kotesovec, Aug 18 2019 *)
Table[Sum[If[k == n, 1, (2^(n - k - 2)*(3 + n - k))] * If[IntegerQ[Sqrt[k]], 1, 0], {k, 1, n}], {n, 0, 30}] (* Vaclav Kotesovec, Aug 18 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2019
STATUS
approved