A279781 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 9/5.

1, -3, 4, -4, 4, -3, -1, 8, -16, 24, -30, 28, -12, -20, 68, -128, 184, -208, 168, -32, -224, 592, -1008, 1344, -1408, 960, 224, -2240, 4928, -7744, 9664, -9216, 4736, 5120, -20608, 39936, -58368, 67840, -57600, 16384, 63488, -180224, 315904, -431104, 463872

Offset: 0

Author

Clark Kimberling, Dec 18 2016

Keywords

• sign
• easy

Comments

If n >= 23, then 32 divides a(n).

Links

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

Crossrefs

Cf. A279634, A279778, A279779, A279780.

Programs

Mathematica

z = 50; f[x_] := f[x] = Sum[Floor[(9/5)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]
LinearRecurrence[{-2,-2,-2,-2},{1,-3,4,-4,4,-3,-1},50] (* Harvey P. Dale, Jul 07 2025 *)

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 9/5.

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