A279628 - OEIS

A279628

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

1, 1, -1, -1, 2, 0, -1, 0, -1, 2, 2, -6, 3, 3, -8, 11, -4, -16, 30, -15, -24, 58, -55, -7, 108, -158, 58, 173, -357, 268, 170, -713, 831, -98, -1235, 2070, -1154, -1641, 4463, -4207, -894, 8392, -11527, 3917, 13077, -26782, 19818, 13765, -54309, 61370, -4901

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OFFSET

0,5

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 = sqrt(3).

MATHEMATICA

z = 100;

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

s = Sqrt[3]; g[x_] := g[x] = Sum[Floor[s*(k + 1)] x^k, {k, 0, z}];

CoefficientList[Series[g[x]/f[x], {x, 0, z}], x]