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

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

Offset

0,1

Links

Table of n, a(n) for n=0..22.

Formula

G(x) = 2*(1-x)/(1-6x-2x^2);

E(x) = (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

Prog

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

Crossrefs

Cf. A083099.

Sequence in context: A363236 A076615 A098777 * A371548 A001119 A216387

Adjacent sequences: A127223 A127224 A127225 * A127227 A127228 A127229

Keyword

easy,nonn

Author

Miklos Kristof, Mar 26 2007

Status

approved