A279593 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = sqrt(5)/2.

1, -2, 1, 0, 0, 0, 0, 0, -1, 3, -3, 1, 0, 0, 0, 0, 0, -1, 3, -3, 1, 0, 0, 0, 1, -4, 5, -1, -2, 1, 0, 0, -1, 6, -14, 15, -6, -1, 1, 0, 0, -1, 7, -18, 21, -10, 0, 1, 1, -7, 18, -18, -3, 20, -13, 1, 0, 9, -34, 68, -72, 29, 13, -15, 2, 0, 11, -48, 107, -127, 69

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = sqrt(5)/2.

Mathematica

z = 30; r = Sqrt[5]/2;
f[x_] := f[x] = Sum[Floor[r*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, 2*z}], x]

Prog

(PARI) r = sqrt(5)/2;
Vec(1/sum(k=0, 70, floor(r*(k + 1))*x^k) + O(x^71)) \\ Indranil Ghosh, Mar 30 2017

Crossrefs

Cf. A279607.

Sequence in context: A279280 A284093 A284095 * A017867 A127843 A350750

Adjacent sequences: A279590 A279591 A279592 * A279594 A279595 A279596

Keyword

sign,easy

Author

Clark Kimberling, Dec 16 2016

Status

approved