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%I #23 Mar 12 2021 22:24:48
%S 1,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
%U 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N Expansion of f(x^1, x^6) in powers of x where f() is Ramanujan's general theta function.
%H Seiichi Manyama, <a href="/A274179/b274179.txt">Table of n, a(n) for n = 0..10000</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 G.f.: f(x, x^6) = Sum_{k in Z} x^((7k^2 + 5k)/2).
%F G.f.: Product_{k>0} (1 + x^(7*k-6)) * (1 + x^(7*k-1)) * (1 - x^(7*k)). - _Michael Somos_, Jan 28 2017
%F a(3*n + 2) = a(5*n + 2) = a(5*n + 3) = 0. - _Michael Somos_, Jan 28 2017
%F a(n) = abs(A232714(n)). - _Michael Somos_, Jan 28 2017
%e G.f. = 1 + x + x^6 + x^9 + x^19 + x^24 + x^39 + x^46 + x^66 + x^75 + x^100 + ...
%e G.f. = q^25 + q^61 + q^241 + q^349 + q^709 + q^889 + q^1429 + q^1681 + q^2401 + ...
%t a[ n_] := If[ n < 0, 0, Boole @ IntegerQ @ Sqrt @ n]; (* _Michael Somos_, Jan 28 2017 *)
%t a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^7] QPochhammer[ -x^6, x^7] QPochhammer[ x^7], {x, 0, n}]; (* _Michael Somos_, Jan 28 2017 *)
%t a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{-1, 1, 0, 0, 0, -1, 1, -1, 0, 0, 0, 1, -1, 1}[[Mod[k, 14, 1]]], {k, n}], {x, 0, n}]; (* _Michael Somos_, Jan 28 2017 *)
%o (PARI) {a(n) = issquare(56*n + 25)}; /* _Michael Somos_, Jan 28 2017 */
%o (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^[1, -1, 1, 0, 0, 0, -1, 1, -1, 0, 0, 0, 1, -1][k%14 + 1], 1 + x * O(x^n)), n))}; /* _Michael Somos_, Jan 28 2017 */
%Y Cf. A232714.
%Y Cf. f(x, x^k): A080995 (k=2), A010054 (k=3), A133100 (k=4), A089801(k=5), this sequence (k=6), A214263 (k=7).
%K nonn
%O 0
%A _Seiichi Manyama_, Jun 12 2016
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