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

0,3

Links

Table of n, a(n) for n=0..31.

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

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 *)

Crossrefs

Cf. A001045.

Sequence in context: A054190 A268681 A101013 * A290997 A052103 A072168

Adjacent sequences: A088685 A088686 A088687 * A088689 A088690 A088691

Keyword

easy,nonn

Author

Paul Barry, Oct 06 2003

Status

approved