A022346 Fibonacci sequence beginning 0, 12.

0, 12, 12, 24, 36, 60, 96, 156, 252, 408, 660, 1068, 1728, 2796, 4524, 7320, 11844, 19164, 31008, 50172, 81180, 131352, 212532, 343884, 556416, 900300, 1456716, 2357016, 3813732, 6170748, 9984480, 16155228, 26139708, 42294936, 68434644, 110729580, 179164224, 289893804, 469058028, 758951832, 1228009860

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000045.

Programs

Mathematica

LinearRecurrence[{1,1},{0,12},40] (* Harvey P. Dale, May 07 2016 *)

PARI

a(n)=12*fibonacci(n) \\ Charles R Greathouse IV, Aug 28 2014

Formula

a(n) = 12*F(n) = F(n+5) + F(n-1) + F(n-3) + F(n-6) for n > 5, where F=A000045.

G.f.: 12*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008

a(n) = F(n+6) + F(n-6) - 6*F(n). - Bruno Berselli, Dec 29 2016