OFFSET
0,2
COMMENTS
Partial sums of A023361.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5254
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: 1/((1 - x)*(1 - Sum_{k>=1} x^(k*(k+1)/2))).
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(`if`(issqr(8*j+1), b(n-j), 0), j=1..n))
end:
a:= proc(n) option remember;
`if`(n<0, 0, b(n)+a(n-1))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Apr 28 2018
MATHEMATICA
nmax = 41; CoefficientList[Series[1/((1 - x) (2 - EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)))), {x, 0, nmax}], x]
nmax = 41; CoefficientList[Series[1/((1 - x) (1 - Sum[x^(k (k + 1)/2), {k, 1, nmax}])), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[SquaresR[1, 8 k + 1] a[n - k], {k, 1, n}]/2; Accumulate[Table[a[n], {n, 0, 41}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 28 2018
STATUS
approved