A127226 a(n) = 2*a(n-1) + 6*a(n-2) with a(0)=2, a(1)=2.

2, 2, 16, 44, 184, 632, 2368, 8528, 31264, 113696, 414976, 1512128, 5514112, 20100992, 73286656, 267179264, 974078464, 3551232512, 12946935808, 47201266688, 172084148224, 627375896576, 2287256682496, 8338768744448, 30401077583872, 110834767634432, 404076000772096

Offset: 0

Author

Miklos Kristof, Mar 26 2007

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (2,6).

Crossrefs

Cf. A083098, A083099.

Programs

Mathematica

a[0]=2;a[1]=2;a[n_]:=2a[n-1]+6a[n-2];Table[a[n],{n,0,22}] (* James C. McMahon, Dec 30 2024 *)

PARI

Vec(2*(1 - x)/(1 - 2*x - 6*x^2) + O(x^31)) \\ Andrew Howroyd, Dec 30 2024

Sage

[lucas_number2(n,2,-6) for n in range(0, 23)] # Zerinvary Lajos, Apr 30 2009

Formula

G.f.: 2*(1 - x)/(1 - 2*x - 6*x^2).

E.g.f.: (exp((1+sqrt(7))*x) + exp((1-sqrt(7))*x));

a(n) = A083099(n) + 6*A083099(n-2).

G.f.: G(0), where G(k)= 1 + 1/(1 - x*(7*k-1)/(x*(7*k+6) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013

a(n) = 2*A083098(n). - Andrew Howroyd, Dec 30 2024

Extensions

a(23) onwards from Andrew Howroyd, Dec 30 2024