A279676 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 5/3.

1, -3, 4, -3, -1, 8, -14, 12, 4, -32, 56, -48, -16, 128, -224, 192, 64, -512, 896, -768, -256, 2048, -3584, 3072, 1024, -8192, 14336, -12288, -4096, 32768, -57344, 49152, 16384, -131072, 229376, -196608, -65536, 524288, -917504, 786432, 262144, -2097152

Offset: 0

Author

Clark Kimberling, Dec 18 2016

Keywords

• sign
• easy

Comments

If n >=11, 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 (-2,-2).

Crossrefs

Cf. A279634, A279675.

Programs

Mathematica

z = 50; f[x_] := f[x] = Sum[Floor[(5/3)*(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 + 2 x + 2 x^2).