A279631 Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = sqrt(2), s = r/(1-r).

3, 0, -2, 2, 0, -2, 4, -4, -2, 10, -10, 0, 14, -24, 16, 18, -56, 54, 10, -102, 142, -54, -154, 332, -256, -158, 666, -768, 90, 1136, -1918, 1086, 1510, -4144, 3912, 814, -7760, 10692, -3690, -12058, 24840, -18478, -12628, 50292, -57022, 4864, 87244, -143424

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 = Sqrt[2]; 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. A001951, A001952.

Sequence in context: A127913 A135991 A331422 * A102003 A176314 A004587

Adjacent sequences: A279628 A279629 A279630 * A279632 A279633 A279634

Keyword

sign,easy

Author

Clark Kimberling, Dec 18 2016

Status

approved