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

0,2

Comments

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

Links

Table of n, a(n) for n=0..23.

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

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.

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 *)

Crossrefs

Sequence in context: A047008 A055990 A211308 * A051924 A272687 A076024

Adjacent sequences: A087942 A087943 A087944 * A087946 A087947 A087948

Keyword

easy,nonn

Author

Paul Barry, Sep 16 2003

Status

approved