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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 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.)