A279630 - OEIS

A279630

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

2, -2, 3, -2, -2, 8, -14, 16, -9, -9, 35, -59, 65, -37, -31, 126, -212, 234, -139, -93, 419, -716, 801, -497, -266, 1346, -2340, 2650, -1695, -757, 4253, -7497, 8563, -5582, -2197, 13336, -23713, 27210, -17901, -6586, 41698, -74419, 85481, -56291, -20491

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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(3), s = r/(1-r).

MATHEMATICA

z = 100;

r = Sqrt[3]; 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]