login
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).
1

%I #4 Dec 17 2016 17:51:31

%S 2,-2,3,-2,-2,8,-14,16,-9,-9,35,-59,65,-37,-31,126,-212,234,-139,-93,

%T 419,-716,801,-497,-266,1346,-2340,2650,-1695,-757,4253,-7497,8563,

%U -5582,-2197,13336,-23713,27210,-17901,-6586,41698,-74419,85481,-56291,-20491

%N 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).

%H Clark Kimberling, <a href="/A279630/b279630.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 = r/(1-r).

%t z = 100;

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

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

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

%Y Cf. A022838, A054406.

%K sign,easy

%O 0,1

%A _Clark Kimberling_, Dec 17 2016