A285484 G.f.: 1/(1 + x/(1 + x^3/(1 + x^6/(1 + x^10/(1 + x^15/(1 + ... + x^(k*(k+1)/2)/(1 + ...))))))), a continued fraction.

1, -1, 1, -1, 2, -3, 4, -6, 9, -13, 18, -26, 38, -54, 77, -111, 160, -229, 328, -472, 679, -974, 1398, -2010, 2888, -4146, 5954, -8555, 12289, -17647, 25346, -36410, 52297, -75109, 107881, -154961, 222574, -319679, 459167, -659528, 947295, -1360612, 1954295, -2807031, 4031809, -5790982

Offset

0,5

Links

Table of n, a(n) for n=0..45.

Formula

a(n) ~ (-1)^n * c * d^n, where d = 1.43632929358192465555987661527... and c = 0.4856490524128736949896673... - Vaclav Kotesovec, Aug 26 2017

Example

G.f.: A(x) = 1 - x + x^2 - x^3 + 2*x^4 - 3*x^5 + 4*x^6 - 6*x^7 + 9*x^8 - 13*x^9 + ...

Mathematica

nmax = 45; CoefficientList[Series[1/(1 + ContinuedFractionK[x^(k (k + 1)/2), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000217, A002105, A206740, A285408.

Sequence in context: A050811 A076968 A238430 * A098889 A061481 A017824

Adjacent sequences: A285481 A285482 A285483 * A285485 A285486 A285487

Keyword

sign

Author

Ilya Gutkovskiy, Apr 19 2017

Status

approved