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A186742 Expansion of f(x, x^11) in powers of x where f(, ) is Ramanujan's general theta function. 4
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 24 sequence [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, ...].

a(n) is the characteristic function of A195818. a(n) = max( 0, -A010815(n + 1)).

G.f.: Sum_{k in Z} x^(6*k^2 - 5*k) = Product_{k>0} (1 + x^(12*k - 11)) * (1 + x^(12*k - 1)) * (1 - x^(12*k)).

Expansion of (f(x, x^2) - f(-x, -x^2)) / (2*x) in powers of x. - Michael Somos, Aug 28 2017

EXAMPLE

G.f. = 1 + x + x^11 + x^14 + x^34 + x^39 + x^69 + x^76 + x^116 + x^125 + ...

G.f. = q^25 + q^49 + q^289 + q^361 + q^841 + q^961 + q^1681 + q^1849 + ...

MATHEMATICA

a[ n_] := With[{m = Sqrt[24 n + 25]}, If[ n >= 0 && IntegerQ @ m, Boole[ Mod[m, 12] == 5 || Mod[m, 12] == 7], 0]]; (* Michael Somos, Aug 28 2017 *)

a[ n_] := SeriesCoefficient[ QPochhammer[ x^12] QPochhammer[ -x^1, x^12] QPochhammer[ -x^11, x^12], {x, 0, n}]; (* Michael Somos, Aug 28 2017 *)

PROG

(PARI) {a(n) = my(m); n++; if( !issquare( 24*n + 1, &m), 0, m%12 == 5 || m%12 == 7)};

(PARI) {a(n) = my(A); n = 3*n + 3; if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 / eta(x + A) - eta(x^3 + A) - x * eta(x^18 + A)^2 / eta(x^9 + A)) / 2, n))}; /* Michael Somos, Aug 28 2017 */

CROSSREFS

Cf. A010815, A195818.

Sequence in context: A016412 A256434 A247133 * A016365 A016426 A014020

Adjacent sequences:  A186739 A186740 A186741 * A186743 A186744 A186745

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 21 2012

STATUS

approved

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)