A171371 a(n) = 6*a(n-1) + 8*a(n-2) with a(1) = 8, a(2) = 18.

8, 18, 172, 1176, 8432, 60000, 427456, 3044736, 21688064, 154486272, 1100422144, 7838423040, 55833915392, 397710876672, 2832936583168, 20179306512384, 143739331739648, 1023870442536960, 7293137309138944, 51949787395129344, 370043822843887616

Offset: 1

Author

Anonymous, Dec 06 2009

Keywords

• nonn
• easy

Comments

Seen on a quiz.

The recurrence was supplied by Zak Seidov, Dec 07 2009.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (6,8).

Programs

Magma

I:=[8,18]; [n le 2 select I[n] else 6*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 18 2011

Mathematica

a[1] = 8; a[2] = 18; a[n_] := a[n] = 6*a[n - 1] + 8*a[n - 2]; Array[a, 20] (* Amiram Eldar, Nov 23 2018 *)

Formula

G.f.: 2*x*(-4 + 15*x)/(-1 + 6*x + 8*x^2). - V.J. Pohjola, Dec 07 2009

a(n) = 8*A189800(n) - 30*A189800(n-1). - R. J. Mathar, Nov 17 2011

From Franck Maminirina Ramaharo, Nov 23 2018: (Start)

a(n) = ((77*sqrt(17) - 255)*(sqrt(17) + 3)^n - (77*sqrt(17) + 255)*(3 - sqrt(17))^n)/136.

E.g.f.: ((77*sqrt(17)*sinh(sqrt(17)*x) - 255*cosh(sqrt(17)*x))*exp(3*x) + 255)/68. (End)

Extensions

More terms from N. J. A. Sloane, Dec 07 2009

G.f. and name adapted to the offset by Bruno Berselli, Apr 04 2011