A022379 Fibonacci sequence beginning 3, 9.
3, 9, 12, 21, 33, 54, 87, 141, 228, 369, 597, 966, 1563, 2529, 4092, 6621, 10713, 17334, 28047, 45381, 73428, 118809, 192237, 311046, 503283, 814329, 1317612, 2131941, 3449553, 5581494, 9031047, 14612541, 23643588, 38256129, 61899717, 100155846, 162055563, 262211409
Offset: 0
Links
- Tanya Khovanova, Recursive Sequences
- Index entries for linear recurrences with constant coefficients, signature (1, 1).
Programs
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Magma
[3*Lucas(n+1): n in [0..40]]; // Bruno Berselli, May 22 2015
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Mathematica
LinearRecurrence[{1, 1}, {3, 9}, 30] (* Alonso del Arte, Oct 09 2013 *) Table[3 LucasL[n + 1], {n, 0, 40}] (* Bruno Berselli, May 22 2015 *) Table[LucasL[n + 4] + LucasL[n - 4] - 4 LucasL[n], {n, 1, 40}] (* Bruno Berselli, Dec 30 2016 *) -
PARI
Vec((3+6*x)/(1-x-x^2)+O(x^99)) \\ Charles R Greathouse IV, Oct 21 2012
Formula
G.f.: (3 + 6*x)/(1 - x - x^2). - Philippe Deléham, Nov 19 2008
a(n+2) = 3*L(n+3) = L(n) + 4*L(n+1) + 2*L(n+2), where L=A000032. - J. M. Bergot, Oct 21 2012
a(n) = Fibonacci(n+4) - Fibonacci(n-4), where n>0 and Fibonacci(-3..-1) = 2,-1,1. - Bruno Berselli, May 22 2015
a(n) = L(n+4) + L(n-4) - 4*L(n) for n>0. - Bruno Berselli, Dec 29 2016
Extensions
More terms from Bruno Berselli, May 22 2015