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A133101 Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan's general theta function. 2
1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 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, 1, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for characteristic functions

FORMULA

The characteristic function of A057569.

Euler transform of period 10 sequence [ 0, 1, 1, -1, -1, -1, 1, 1, 0, -1, ...].

G.f.: Prod_{k>0} (1 - x^(5*k)) * (1 + x^(5*k - 2)) * (1 + x^(5*k - 3)) = Sum_{k in Z} x^((5*k^2 + k) / 2).

a(n) = abs(A113428(n)).

EXAMPLE

G.f. = 1 + x^2 + x^3 + x^9 + x^11 + x^21 + x^24 + x^38 + x^42 + x^60 + x^65 + ...

G.f. = q + q^81 + q^121 + q^361 + q^441 + q^841 + q^961 + q^1521 + q^1681 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2, x^5] QPochhammer[ -x^3, x^5] QPochhammer[ x^5], {x, 0, n}]; (* Michael Somos, Oct 31 2015 *)

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, 1 + x^k*[ -1, 0, 1, 1, 0][k%5 + 1], 1 + x * O(x^n)), n))};

CROSSREFS

Cf. A057569, A113428.

Sequence in context: A267878 A231367 A113428 * A258769 A266377 A266326

Adjacent sequences:  A133098 A133099 A133100 * A133102 A133103 A133104

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 11 2007

STATUS

approved

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Last modified November 15 06:05 EST 2019. Contains 329144 sequences. (Running on oeis4.)