%I #4 Dec 17 2016 17:51:24

%S 1,-1,2,-2,1,1,-5,10,-13,11,-1,-18,41,-57,53,-17,-53,140,-208,207,-92,

%T -146,454,-708,735,-380,-396,1427,-2307,2467,-1390,-1077,4421,-7346,

%U 8018,-4749,-2997,13634,-23075,25501,-15523,-8632,42051,-71931,79989,-49260

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

%H Clark Kimberling, <a href="/A279629/b279629.txt">Table of n, a(n) for n = 0..1000</a>

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

%t z = 100;

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

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

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

%Y Cf. A001951, A022838, A279628.

%K sign,easy

%O 0,3

%A _Clark Kimberling_, Dec 17 2016