A304633 Expansion of 2/((1 - x)*(3 + 2*x - theta_3(x))), where theta_3() is the Jacobi theta function.

1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 7, 7, 7, 9, 12, 13, 13, 16, 20, 23, 23, 27, 35, 41, 42, 47, 61, 71, 75, 82, 104, 124, 134, 146, 178, 217, 237, 258, 307, 377, 419, 456, 535, 651, 739, 804, 933, 1126, 1300, 1422, 1629, 1955, 2275, 2513, 2846, 3397, 3972, 4435, 4990, 5904

Offset

0,5

Comments

Partial sums of A280542.

Links

Table of n, a(n) for n=0..62.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Formula

G.f.: 1/((1 - x)*(1 - Sum_{k>=2} x^(k^2))).

Mathematica

nmax = 62; CoefficientList[Series[2/((1 - x) (3 + 2 x - EllipticTheta[3, 0, x])), {x, 0, nmax}], x]
nmax = 62; CoefficientList[Series[1/((1 - x) (1 - Sum[x^k^2, {k, 2, nmax}])), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Boole[IntegerQ[k^(1/2)] && k != 1] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 62}]]

Crossrefs

Cf. A000290, A001156, A006456, A010052, A248801, A280542, A302833, A303667.

Sequence in context: A321423 A035451 A363337 * A124746 A124789 A103372

Adjacent sequences: A304630 A304631 A304632 * A304634 A304635 A304636

Keyword

nonn

Author

Ilya Gutkovskiy, May 15 2018

Status

approved