A097133 a(n) = 3*Fibonacci(n) + (-1)^n.

1, 2, 4, 5, 10, 14, 25, 38, 64, 101, 166, 266, 433, 698, 1132, 1829, 2962, 4790, 7753, 12542, 20296, 32837, 53134, 85970, 139105, 225074, 364180, 589253, 953434, 1542686, 2496121, 4038806, 6534928, 10573733, 17108662, 27682394, 44791057, 72473450, 117264508

Offset: 0

Author

Paul Barry, Jul 26 2004

Keywords

• easy
• nonn

Comments

Binomial transform is A097134.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Crossrefs

Cf. A000045, A097134, A097136.

Programs

Haskell

a097133 n = a097133_list !! n
a097133_list = 1 : 2 : 4 : zipWith (+)
               (map (* 2) $ tail a097133_list) a097133_list
-- Reinhard Zumkeller, Feb 24 2015

Mathematica

CoefficientList[Series[(1+2x+2x^2)/((1+x)(1-x-x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{0,2,1},{1,2,4},40] (* Harvey P. Dale, May 07 2011 *)

Formula

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

a(n) = 2*a(n-2)+a(n-3);

a(2*n) = 3*F(2*n)+1 = A097136(n).