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 A245552 G.f.: Sum_{n>=0} (2*n+1)*x^(n^2+n+1). 3

%I

%S 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,

%T 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,

%U 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

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

%C Related to g.f. for A053187.

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

%H Antti Karttunen, <a href="/A245552/b245552.txt">Table of n, a(n) for n = 0..10101</a>

%F a(2*n+1) = A198954(n), a(2*n) = 0.- _Robert Israel_, Aug 05 2014

%t Join[{0},Flatten[Table[Join[{n,PadRight[{},n,0]}],{n,1,19,2}]]] (* _Harvey P. Dale_, Dec 14 2014 *)

%o (PARI)

%o A198954(n) = { my(m); if(issquare(8*n + 1, &m), m, 0) }; \\ This function from _Michael Somos_

%o A245552(n) = if(!(n%2),0,A198954((n-1)/2)); \\ After _Robert Israel_'s formula - _Antti Karttunen_, Jul 24 2017

%Y Cf. A002483, A053187, A198954.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Aug 02 2014

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)