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A153873 a(n) = 9*Fibonacci(2n+1) - 1. 5
8, 17, 44, 116, 305, 800, 2096, 5489, 14372, 37628, 98513, 257912, 675224, 1767761, 4628060, 12116420, 31721201, 83047184, 217420352, 569213873, 1490221268, 3901449932, 10214128529, 26740935656, 70008678440, 183285099665, 479846620556, 1256254762004, 3288917665457 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

FORMULA

a(n) = 3*a(n-1) - a(n-2) + 1.

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).

a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).

a(n) = 9*A001519(n+1) - 1.

a(n) = -1 + (9/2)*(((3/2)+(1/2)*sqrt(5))^n + ((3/2)-(1/2)*sqrt(5))^n) + (9/10)*sqrt(5)*(((3/2)+(1/2)*sqrt(5))^n - ((3/2)-(1/2)*sqrt(5))^n), with n>=0. Paolo P. Lava, Jan 20 2009

G.f.: (8 - 15*x + 8*x^2)/((1-x)*(1-3*x+x^2)). - Jaume Oliver Lafont, Aug 30 2009

MATHEMATICA

LinearRecurrence[{4, -4, 1}, {8, 17, 44}, 25] (* G. C. Greubel, Aug 31 2016 *)

PROG

(MAGMA) [9*Fibonacci(2*n+1)-1: n in [0..30]]; // Vincenzo Librandi, Aug 07 2011

(PARI) a(n)=9*fibonacci(2*n+1)-1 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Sequence in context: A041849 A041124 A048695 * A111325 A173056 A008782

Adjacent sequences:  A153870 A153871 A153872 * A153874 A153875 A153876

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jan 03 2009

STATUS

approved

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Last modified November 14 06:40 EST 2019. Contains 329110 sequences. (Running on oeis4.)