A088688 Binomial transform of A088689.

0, 1, 3, 6, 12, 27, 63, 141, 297, 594, 1146, 2169, 4095, 7827, 15291, 30582, 62256, 127791, 262143, 534129, 1078101, 2156202, 4282878, 8477181, 16777215, 33288711, 66311703, 132623406, 266043972, 534479427, 1073741823, 2154658101

Offset: 0

Author

Paul Barry, Oct 06 2003

Keywords

• easy
• nonn
• changed

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6).

Crossrefs

Cf. A001045.

Programs

Mathematica

Table[Sum[Binomial[n,k] * Mod[k*Floor[3*(k+1)/2] - 2*k, 3], {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 30 2017 *)
CoefficientList[Series[-x(1-3x+3x^2+x^3)/((2x-1)(x^2-x+1)(3x^2-3x+1)),{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6},{0,1,3,6,12},40] (* Harvey P. Dale, Aug 28 2025 *)

Formula

a(n) = 2^n - cos(Pi*n/3) - 3^(n/2)*sin(Pi*n/6)/sqrt(3).

O.g.f.: -x(1-3x+3x^2+x^3)/[(2x-1)(x^2-x+1)(3x^2-3x+1)]. - R. J. Mathar, Apr 02 2008