A153873 a(n) = 9*Fibonacci(2n+1) - 1.
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
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
Programs
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Magma
[9*Fibonacci(2*n+1)-1: n in [0..30]]; // Vincenzo Librandi, Aug 07 2011
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Mathematica
LinearRecurrence[{4,-4,1}, {8,17,44}, 25] (* G. C. Greubel, Aug 31 2016 *) -
PARI
a(n)=9*fibonacci(2*n+1)-1 \\ Charles R Greathouse IV, Oct 07 2015
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.
G.f.: (8 - 15*x + 8*x^2)/((1-x)*(1-3*x+x^2)). - Jaume Oliver Lafont, Aug 30 2009