A132397 Second trisection of A024494.

2, 10, 86, 682, 5462, 43690, 349526, 2796202, 22369622, 178956970, 1431655766, 11453246122, 91625968982, 733007751850, 5864062014806, 46912496118442, 375299968947542, 3002399751580330, 24019198012642646, 192153584101141162

Offset: 0

Author

Paul Curtz, Nov 20 2007

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,8).

Crossrefs

Cf. A082311, A132805, A078008.

Programs

Mathematica

CoefficientList[Series[2(2x-1)/((x+1)(8x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{7,8},{2,10},30] (* Harvey P. Dale, Oct 14 2015 *)

PARI

Vec(2*(1 - 2*x) / ((1 + x)*(1 - 8*x)) + O(x^20)) \\ Colin Barker, Jun 05 2020

Formula

O.g.f.: 2(2x-1)/((x+1)(8x-1)). a(n) = 2*A082311(n). - R. J. Mathar, Jan 13 2008

a(0)=2, a(1)=10, a(n) = 7*a(n-1)+8*a(n-2). - Harvey P. Dale, Oct 14 2015

From Oboifeng Dira, Jun 05 2020: (Start)

a(n) = A078008(3*n+2). Third trisection of A078008.

a(n) = Sum_{k=0..n} binomial(3*n+2,3*k+1).

(End)

a(n) = 2*((-1)^n + 2^(1+3*n)) / 3 for n>1. - Colin Barker, Jun 05 2020

Extensions

More terms from R. J. Mathar, Jan 13 2008