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A281814 Expansion of f(x, x^8) in powers of x where f(, ) is Ramanujan's general theta function. 5
1, 1, 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, 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, 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, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

f(x,x^m) = 1 + Sum_k=1..oo} x^((m+1)*k*(k-1)/2) (x^k + x^(m*k)). - N. J. A. Sloane, Jan 30 2017

Euler transform of period 18 sequence [1, -1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, -1, 1, -1, ...].

Characterisctic function of generalized 11-gonal numbers A195160.

G.f.: Sum_{k in Z} x^(k*(9*k + 7)/2).

G.f.: Product_{k>0} (1 + x^(9*k-8)) * (1 + x^(9*k-1)) * (1 - x^(9*k)).

EXAMPLE

G.f. = 1 + x + x^8 + x^11 + x^25 + x^30 + x^51 + x^58 + x^86 + x^95 + ...

G.f. = q^49 + q^121 + q^625 + q^841 + q^1849 + q^2209 + q^3721 + q^4225 + ...

MATHEMATICA

a[ n_] := SquaresR[ 1, 72 n + 49] / 2;

a[ n_] := If[ n < 0, 0, Boole @ IntegerQ @ Sqrt @ (72 n + 49)];

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^9] QPochhammer[ -x^8, x^9] QPochhammer[ x^9], {x, 0, n}];

PROG

(PARI) {a(n) = issquare(72*n + 49)};

CROSSREFS

Cf. f(x, x^k) for k=2..11: A080995, A010054, A133100, A089801, A274179, A214263, A281814, A205988, A281815, A186742.

Cf. A195160, A281490.

Sequence in context: A167700 A010057 A204220 * A279484 A279329 A292438

Adjacent sequences:  A281811 A281812 A281813 * A281815 A281816 A281817

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 30 2017

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)