

A245552


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


3



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
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OFFSET

0,4


COMMENTS

Related to g.f. for A053187.
Apart from signs and a factor of 2, this is the classical Jacobi thetafunction 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((n1)/2)); \\ After Robert Israel's formula  Antti Karttunen, Jul 24 2017


CROSSREFS

Cf. A002483, A053187, A198954.
Sequence in context: A096133 A293381 A118112 * A195938 A184762 A081805
Adjacent sequences: A245549 A245550 A245551 * A245553 A245554 A245555


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Aug 02 2014


STATUS

approved



