A245552 G.f.: Sum_{n>=0} (2*n+1)*x^(n^2+n+1).

0, 1, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19

Offset

0,4

Comments

Related to g.f. for A053187.

Apart from signs and a factor of 2, this is the classical Jacobi theta-function theta'_1(q), see A002483.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10101

Formula

a(2*n+1) = A198954(n), a(2*n) = 0.- Robert Israel, Aug 05 2014

Mathematica

Join[{0}, Flatten[Table[Join[{n, PadRight[{}, n, 0]}], {n, 1, 19, 2}]]] (* Harvey P. Dale, Dec 14 2014 *)

Prog

(PARI)
A198954(n) = { my(m); if(issquare(8*n + 1, &m), m, 0) }; \\ This function from Michael Somos
A245552(n) = if(!(n%2), 0, A198954((n-1)/2)); \\ After Robert Israel's formula - Antti Karttunen, Jul 24 2017

Crossrefs

Cf. A002483, A053187, A198954.

Sequence in context: A349379 A293381 A118112 * A195938 A184762 A330734

Adjacent sequences: A245549 A245550 A245551 * A245553 A245554 A245555

Keyword

nonn

Author

N. J. A. Sloane, Aug 02 2014

Status

approved