A293268 G.f.: Re(1/(1 + i*x/(1 + i*x^2/(1 + i*x^3/(1 + i*x^4/(1 + i*x^5/(1 + ...))))))), a continued fraction, where i is the imaginary unit.

1, 0, -1, -1, 1, 3, 2, -2, -7, -6, 4, 16, 14, -9, -37, -33, 20, 87, 82, -41, -201, -198, 85, 465, 475, -178, -1084, -1150, 353, 2511, 2767, -684, -5810, -6633, 1287, 13463, 15923, -2222, -31119, -38130, 3356, 71838, 91138, -3595, -165763, -217705, -1761, 381895, 519284, 27984, -878685

Offset: 0

Author

Ilya Gutkovskiy, Oct 04 2017

Keywords

• sign

Examples

			G.f. A(x) = Sum_{n>=0} (a(n) + i*A293269(n))*x^n = 1 - i*x - x^2 - (1 - i)*x^3 + (1 + 2*i)*x^4 + 3*x^5 + (2 - 3*i)*x^6 - (2 + 5*i)*x^7 - (7 + i)*x^8 - ...
		

Links

• Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Crossrefs

Cf. A007325, A278399, A292136, A293269.

Programs

Mathematica

nmax = 50; Re[CoefficientList[Series[1/(1 + ContinuedFractionK[I x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]]
nmax = 50; Re[CoefficientList[Series[Sum[I^k x^(k (k + 1)) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}] / Sum[I^k x^(k^2) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]]

Formula

G.f.: Re( (Sum_{k>=0} i^k*x^(k*(k+1))/Product_{m=1..k} (1 - x^m)) / (Sum_{k>=0} i^k*x^(k^2)/Product_{m=1..k} (1 - x^m)) ), where i is the imaginary unit.