A279629 Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = sqrt(3), s = sqrt(2).

1, -1, 2, -2, 1, 1, -5, 10, -13, 11, -1, -18, 41, -57, 53, -17, -53, 140, -208, 207, -92, -146, 454, -708, 735, -380, -396, 1427, -2307, 2467, -1390, -1077, 4421, -7346, 8018, -4749, -2997, 13634, -23075, 25501, -15523, -8632, 42051, -71931, 79989, -49260

Offset

0,3

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 = sqrt(2).

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

Crossrefs

Cf. A001951, A022838, A279628.

Sequence in context: A219727 A177694 A092450 * A309575 A014291 A136587

Adjacent sequences: A279626 A279627 A279628 * A279630 A279631 A279632

Keyword

sign,easy

Author

Clark Kimberling, Dec 17 2016

Status

approved