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A214264 Expansion of f(x^3, x^5) in powers of x where f() is Ramanujan's two-variable theta function. 6
1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 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 (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

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 16 sequence [ 0, 0, 1, 0, 1, -1, 0, -1, 0, -1, 1, 0, 1, 0, 0, -1, ...].

G.f.: Sum_{k} x^(((8*k + 1)^2 - 1) / 16).

Characteristic function of A074378. a(n) = 1 if and only if n is in A074378.

a(n) = A010054(2*n).

EXAMPLE

1 + x^3 + x^5 + x^14 + x^18 + x^33 + x^39 + x^60 + x^68 + x^95 + x^105 +

q + q^49 + q^81 + q^225 + q^289 + q^529 + q^625 + q^961 + q^1089 + ...

MATHEMATICA

f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A214264[n_] := SeriesCoefficient[f[x^3, x^5], {x, 0, n}]; Table[A214264[n], {n, 0, 50}] (* G. C. Greubel, Dec 03 2017 *)

PROG

(PARI) {a(n) = issquare( 16*n + 1)}

CROSSREFS

Cf. A010054, A047522, A074378.

Sequence in context: A273511 A104015 A244465 * A173858 A217586 A101266

Adjacent sequences:  A214261 A214262 A214263 * A214265 A214266 A214267

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 09 2012

STATUS

approved

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Last modified July 25 03:36 EDT 2021. Contains 346282 sequences. (Running on oeis4.)