A045826 a(n) = A005887(n) / 2.

3, 4, 12, 0, 15, 12, 12, 0, 24, 12, 24, 0, 15, 16, 36, 0, 24, 24, 12, 0, 48, 12, 36, 0, 27, 24, 36, 0, 24, 36, 36, 0, 48, 12, 48, 0, 24, 28, 48, 0, 51, 36, 24, 0, 72, 24, 24, 0, 24, 36, 84, 0, 48, 36

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

Expansion of q^(-1) * (phi^3(q) - phi^3(-q)) / 4 in powers of q^2 where phi() is a Ramanujan theta function. - Michael Somos, Mar 12 2011

A005875(2*n + 1) = 2 * a(n). - Michael Somos, Mar 12 2011

Example

3 + 4*x + 12*x^2 + 15*x^4 + 12*x^5 + 12*x^6 + 24*x^8 + 12*x^9 + ...
3*q + 4*q^3 + 12*q^5 + 15*q^9 + 12*q^11 + 12*q^13 + 24*q^17 + 12*q^19 + ...

Mathematica

A005887[n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q]^3 - EllipticTheta[3, 0, -q]^3)/(2 q), {q, 0, n}];  Table[A005887[n]/2, {n, 0, 50}][[1;; ;; 2]] (* G. C. Greubel, Feb 09 2018 *)

Prog

(PARI) {a(n) = if( n<0, 0, n = 2*n + 1; polcoeff( sum( k=1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^3 / 2, n))} /* Michael Somos, Mar 12 2011 */

Crossrefs

Cf. A005875, A005887.

Sequence in context: A041299 A001112 A042079 * A346471 A084200 A348997

Adjacent sequences: A045823 A045824 A045825 * A045827 A045828 A045829

Keyword

nonn

Author

N. J. A. Sloane

Status

approved