A247133 - OEIS

%I #21 Mar 12 2021 22:24:47

%S 1,-1,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0

%N Expansion of f(-x, -x^11) in powers of x where f() is a Ramanujan theta function

%H Seiichi Manyama, <a href="/A247133/b247133.txt">Table of n, a(n) for n = 0..1000</a>

%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>

%F Euler transform of period 12 sequence [ -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, ...].

%F G.f.: Product_{k>0} (1 - x^(12*k)) * (1 - x^(12*k - 1)) * (1 - x^(12*k - 11)).

%F Convolution inverse of A210964.

%e G.f. = 1 - x - x^11 + x^14 + x^34 - x^39 - x^69 + x^76 + x^116 - x^125 + ...

%e G.f. = q^25 - q^49 - q^289 + q^361 + q^841 - q^961 - q^1681 + q^1849 + ...

%o (PARI) {a(n) = my(m = 24*n + 25); if( issquare(m, &m) && (m%12==5 || m%12==7), (-1)^((m+6) \ 12))};

%Y Cf. A210964.

%K sign

%O 0,1

%A _Michael Somos_, Jan 10 2015