A294922 Expansion of 1/(1 + x/(1 + x^3/(1 + x^4/(1 + x^7/(1 + x^11/(1 + ... + x^Lucas(k)/(1 + ...))))))), a continued fraction.

1, -1, 1, -1, 2, -3, 4, -6, 8, -11, 16, -22, 31, -44, 61, -85, 119, -166, 232, -325, 454, -634, 886, -1237, 1728, -2415, 3373, -4712, 6583, -9194, 12843, -17941, 25060, -35006, 48899, -68303, 95409, -133272, 186159, -260036, 363230, -507373, 708720, -989969, 1382827, -1931590

Offset: 0

Author

Ilya Gutkovskiy, Nov 16 2017

Keywords

• sign

Crossrefs

Cf. A000204, A007325, A206741, A206742, A206743, A279586.

Programs

Mathematica

nmax = 45; CoefficientList[Series[1/(1 + ContinuedFractionK[x^LucasL[k], 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 + x/(1 + x^3/(1 + x^4/(1 + x^7/(1 + x^11/(1 + ... + x^A000204(k)/(1 + ...))))))), a continued fraction.