A279632 Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e - 1, s = r/(1-r).

2, -2, 3, -2, -2, 8, -14, 17, -12, -5, 34, -68, 91, -80, 11, 126, -308, 467, -488, 235, 382, -1316, 2291, -2760, 1995, 638, -5220, 10738, -14725, 13447, -3007, -18467, 47914, -74806, 80821, -43890, -51936, 201548, -363193, 450980, -347117, -55972, 782359

Offset

0,1

Links

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

Formula

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

Mathematica

z = 100;
r = E - 1; f[x_] := f[x] = Sum[Floor[r*(k + 1)] x^k, {k, 0, z}];
s = r/(r - 1); g[x_] := g[x] = Sum[Floor[s*(k + 1)] x^k, {k, 0, z}]
CoefficientList[Series[g[x]/f[x], {x, 0, z}], x]

Crossrefs

Cf. A000210, A054385.

Sequence in context: A225637 A185268 A279630 * A363680 A300817 A341417

Adjacent sequences: A279629 A279630 A279631 * A279633 A279634 A279635

Keyword

sign,easy

Author

Clark Kimberling, Dec 18 2016

Status

approved