A176812 Expansion of 3*(1+x)/(1-2*x-5*x^2).

3, 9, 33, 111, 387, 1329, 4593, 15831, 54627, 188409, 649953, 2241951, 7733667, 26677089, 92022513, 317430471, 1094973507, 3777099369, 13029066273, 44943629391, 155032590147, 534783327249, 1844729605233, 6363375846711

Offset: 0

Author

Roger L. Bagula, Apr 26 2010

Keywords

• nonn
• easy

Comments

Binomial transform of A026532 after dropping A026532(0). [From R. J. Mathar, Apr 27 2010]

Links

• Index entries for linear recurrences with constant coefficients, signature (2,5).

Programs

Mathematica

a[n_] = 2^n*(((3 + Sqrt[ 6])/2)*((1 + Sqrt[6])/2)^n + ((3 - Sqrt[6])/2)*((1 - Sqrt[6])/2)^n); Table[FullSimplify[a[n]], {n, 0, 30}]
CoefficientList[Series[(-3(1+x))/(5x^2+2x-1),{x,0,40}],x]  (* Harvey P. Dale, Feb 24 2011 *)

Formula

Binet form: a(n)=2^n*(((3 + Sqrt[6])/2)*((1 + Sqrt[6])/2)^n + ((3 - Sqrt[6])/2)*((1 - Sqrt[6])/2)^n) = 3*A180168(n).