A087945 Expansion of (1-2x-x^2)/((1-2x)(1-4x+x^2)).

1, 4, 14, 50, 182, 670, 2482, 9226, 34358, 128078, 477698, 1782202, 6650086, 24816094, 92610194, 345616490, 1289839382, 4813708270, 17964928162, 67045873306, 250218302918, 933826814078, 3485087904818, 13006522708042

Offset: 0

Author

Paul Barry, Sep 16 2003

Keywords

• easy
• nonn

Comments

First differences of A087944. Binomial transform of A052948(n+1). a(n)=(2/3)A001834+2^n/3.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-9,2).

Programs

Mathematica

CoefficientList[Series[(1-2x-x^2)/((1-2x)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{6,-9,2},{1,4,14},30] (* Harvey P. Dale, Aug 21 2021 *)

Formula

a(0)=1, a(2)=4, a(2)=14, a(n)=6a(n-1)-9a(n-2)+2a(n-3), n>2; a(n)=(2^n+(1-sqrt(3))(2-sqrt(3))^n+(1+sqrt(3))(2+sqrt(3))^n)/3.