OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3312
FORMULA
G.f.: Sum_{k>=1} x^(k*(k+1)/2)*(1-x)^2/(1-2*x)^2.
a(n) ~ c * 2^n * n, where c = 0.1604081401637884665734606925563573585565153844... - Vaclav Kotesovec, Aug 18 2019
EXAMPLE
a(4) = 14: (1)(1)(1)(1), 2(1)(1), (1)2(1), (1)(1)2, 22, (3)(1), (1)(3), 4.
MAPLE
a:= proc(n) option remember; add(a(n-j)+
`if`(issqr(8*j+1), ceil(2^(n-j-1)), 0), j=1..n)
end:
seq(a(n), n=0..33);
MATHEMATICA
CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2*x^(1/8)) - 1)*((1 - x)^2/(1 - 2*x)^2), {x, 0, 30}], x] (* Vaclav Kotesovec, Aug 18 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2019
STATUS
approved