A306575 Expansion of 1/(1 - x - x^2/(1 - x^2 - x^3/(1 - x^3 - x^4/(1 - x^4 - x^5/(1 - ...))))), a continued fraction.
1, 1, 2, 3, 6, 11, 21, 40, 77, 148, 285, 550, 1061, 2049, 3957, 7644, 14768, 28535, 55138, 106549, 205902, 397906, 768967, 1486070, 2871932, 5550233, 10726300, 20729542, 40061784, 77423250, 149628008, 289170949, 558851751, 1080037175, 2087280839, 4033881485
Offset: 0
Keywords
Programs
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Mathematica
nmax = 35; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x^k, 1 - x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
Formula
a(n) ~ c * d^n, where d = 1.9326019136649450138850556203... and c = 0.389707331111778150048054243... - Vaclav Kotesovec, Jul 01 2019