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

1,1

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).

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)

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 *)

Prog

(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

Crossrefs

Sequence in context: A219524 A259852 A215174 * A092692 A338474 A001151

Adjacent sequences: A171368 A171369 A171370 * A171372 A171373 A171374

Keyword

nonn,easy

Author

Anonymous, Dec 06 2009

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

Status

approved