A127262 a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 12*a(n-2).

2, 2, 28, 80, 496, 1952, 9856, 43136, 204544, 926720, 4307968, 19736576, 91168768, 419176448, 1932378112, 8894873600, 40978284544, 188695052288, 869129519104, 4002599665664, 18434753560576, 84900703109120

Offset: 0

Author

Miklos Kristof, Mar 27 2007

Keywords

• easy
• nonn

Comments

If A091914(n-1)=F(n) the Fibonacci-like sequence, then a(n) is the Lucas-type sequence.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,12).

Crossrefs

Cf. A091914, A125816.

Programs

Maple

a[0]:=2:a[1]:=2:for i from 2 to 40 do a[i]:=2*a[i-1]+12*a[i-2] od: seq(a[n],n=0..40);

Mathematica

LinearRecurrence[{2,12},{2,2},30] (* Harvey P. Dale, May 24 2017 *)

Sage

[lucas_number2(n,2,-12) for n in range(0, 22)] # Zerinvary Lajos, Apr 30 2009

Formula

a(n) = ((1+sqrt(13))^n - (1-sqrt(13)^n))/(2*sqrt(13)).

G.f.: 2*(1-x)/(1-2*x-12*x^2).

E.g.f.: exp((1+sqrt(13))*x) + exp((1-sqrt(13))*x).

a(n) = A091914(n) + 12*A091914(n-2).

a(n) = 2*A125816(n). - Alois P. Heinz, Mar 03 2018