A279675 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 4/3.

1, -2, 0, 3, -2, -4, 8, 0, -16, 16, 16, -48, 16, 80, -112, -48, 272, -176, -368, 720, 16, -1456, 1424, 1488, -4336, 1360, 7312, -10032, -4592, 24656, -15472, -33840, 64784, 2896, -132464, 126672, 138256, -391600, 115088, 668112, -898288, -437936, 2234512

Offset: 0

Author

Clark Kimberling, Dec 18 2016

Keywords

• sign
• easy

Comments

If n >=7, then 16 divides a(n).

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,-2).

Crossrefs

Cf. A279634, A279676.

Programs

Mathematica

z = 50; f[x_] := f[x] = Sum[Floor[(4/3)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/(1 + 2x + 4x^2 + 5x^3 + 6x^4 + 8x^5 + ...).

G.f.: (1 - x) (1 - x^3)/(1 + x + 2 x^2).