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