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A186741 Expansion of f(x^5, x^7) in powers of x where f(, ) is Ramanujan's general theta function. 1
1, 0, 0, 0, 0, 1, 0, 1, 0, 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, 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, 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 (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..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

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

a(n) is the characteristic function of A036498. a(n) = max( 0, A010815(n)).

G.f.: Sum_{k in Z} x^(6*k^2 - k) = Product_{k>0} (1 + x^(12*k - 7)) * (1 + x^(12*k - 5)) * (1 - x^(12*k)).

EXAMPLE

G.f. = 1 + x^5 + x^7 + x^22 + x^26 + x^51 + x^57 + x^92 + x^100 + x^145 + ...

G.f. = q + q^121 + q^169 + q^529 + q^625 + q^1225 + q^1369 + q^2209 + q^2401 + ...

MATHEMATICA

a[n_]:= SeriesCoefficient[ QPochhammer[-q^5, q^12]*QPochhammer[-q^7, q^12] *QPochhammer[q^12, q^12], {q, 0, n}]; (* G. C. Greubel, dec 08 2017 *)

PROG

(PARI) {a(n) = my(m); if( !issquare( 24*n + 1, &m), 0, m%12 == 1 || m%12 == 11)};

CROSSREFS

Cf. A010815, A036498, A247223.

Sequence in context: A027356 A181663 A247223 * A173864 A353348 A353350

Adjacent sequences: A186738 A186739 A186740 * A186742 A186743 A186744

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 21 2012

STATUS

approved

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Last modified November 29 08:47 EST 2022. Contains 358422 sequences. (Running on oeis4.)