A099215 a(n)=4a(n-1)-4a(n-2)+3a(n-3).

1, 2, 4, 11, 34, 104, 313, 938, 2812, 8435, 25306, 75920, 227761, 683282, 2049844, 6149531, 18448594, 55345784, 166037353, 498112058, 1494336172, 4483008515, 13449025546, 40347076640, 121041229921, 363123689762, 1089371069284

Offset: 0

Author

Paul Barry, Oct 06 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-4,3).

Crossrefs

Cf. A099214.

Programs

Mathematica

LinearRecurrence[{4,-4,3},{1,2,4},30] (* Harvey P. Dale, Mar 02 2013 *)

Formula

G.f.: (1-2x)/((1-2x)^2-3x^3); a(n)=sum{k=0..floor(n/3), binomial(n-k, 2k)3^k*2^(n-3k)}.

a{x}=1/7(-Cos[(Pi*x)/3]+Cosh[x*Log[3]]+3*Sqrt[3]*Sin[(Pi*x)/3]+Sinh[x*Log[3]]) - Harvey P. Dale, Mar 02 2013