A097135 a(0) = 1; for n>0, a(n) = 3*Fibonacci(n).

1, 3, 3, 6, 9, 15, 24, 39, 63, 102, 165, 267, 432, 699, 1131, 1830, 2961, 4791, 7752, 12543, 20295, 32838, 53133, 85971, 139104, 225075, 364179, 589254, 953433, 1542687, 2496120, 4038807, 6534927, 10573734, 17108661, 27682395, 44791056, 72473451, 117264507

Offset: 0

Author

Paul Barry, Jul 26 2004

Keywords

• nonn
• easy

Comments

Binomial transform is A097136.

Links

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

Crossrefs

Cf. A000032, A000045.

Essentially the same as A022086.

Programs

Mathematica

Join[{1}, Table[3*Fibonacci[n], {n, 70}]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2012 *)

PARI

a(n)=if(n,3*finonacci(n),1) \\ Charles R Greathouse IV, Oct 16 2015

Formula

G.f. : (1+2*x-x^2)/(1-x-x^2).

a(n) = a(n-1)+a(n-2) for n>2.

a(2n) = A097134(n); a(2n+1) = 3*F(2n+1).

Extensions

Definition rewritten by N. J. A. Sloane, Jan 24 2010