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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,8).

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

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 *)

Prog

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

Crossrefs

Cf. A082311, A132805, A078008.

Sequence in context: A332655 A156466 A304403 * A202745 A364396 A367372

Adjacent sequences: A132394 A132395 A132396 * A132398 A132399 A132400

Keyword

nonn,easy

Author

Paul Curtz, Nov 20 2007

Extensions

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

Status

approved