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A281815 Expansion of f(x, x^10) in powers of x where f(, ) is Ramanujan's general theta function. 4
1, 1, 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, 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, 1, 0, 0, 0, 0, 0, 0, 1, 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

LINKS

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

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 22 sequence [1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, ...].

Characterisctic function of generalized 13-gonal numbers A195313.

G.f.: Sum_{k in Z} x^(k*(11*k + 9)/2).

G.f.: Product_{k>0} (1 + x^(11*k-10)) * (1 + x^(11*k-1)) * (1 - x^(11*k)).

EXAMPLE

G.f. = 1 + x + x^10 + x^13 + x^31 + x^36 + x^63 + x^70 + x^106 + x^115 + ...

G.f. = q^81 + q^169 + q^961 + q^1225 + q^2809 + q^3249 + q^5625 + q^6241 + ...

MATHEMATICA

a[ n_] := SquaresR[ 1, 88 n + 81] / 2;

a[ n_] := If[ n < 0, 0, Boole @ IntegerQ @ Sqrt @ (88 n + 81)];

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^11] QPochhammer[ -x^10, x^11] QPochhammer[ x^11], {x, 0, n}];

PROG

(PARI) {a(n) = issquare(88*n + 81)};

CROSSREFS

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

Cf. A195313.

Sequence in context: A016394 A016335 A016373 * A205988 A167700 A010057

Adjacent sequences:  A281812 A281813 A281814 * A281816 A281817 A281818

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 30 2017

STATUS

approved

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Last modified September 17 19:16 EDT 2019. Contains 327137 sequences. (Running on oeis4.)