A087944 Expansion of (1-4*x+3*x^2)/((1-2*x)*(1-4*x+x^2)).

1, 2, 6, 20, 70, 252, 922, 3404, 12630, 46988, 175066, 652764, 2434966, 9085052, 33901146, 126511340, 472127830, 1761967212, 6575675482, 24540603644, 91586476950, 341804779868, 1275631593946, 4760719498764, 17767242206806

Offset: 0

Author

Paul Barry, Sep 16 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A052948.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-9,2).

Crossrefs

Cf. A052948.

Programs

Mathematica

CoefficientList[Series[(1-4x+3x^2)/((1-2x)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{6,-9,2},{1,2,6},30] (* Harvey P. Dale, Feb 09 2013 *)

Formula

a(0)=1, a(2)=2, a(2)=6, a(n) = 6*a(n-1)-9*a(n-2)+2*a(n-3), n>2.

a(n) = (2^n+(2+sqrt(3))^n+(2-sqrt(3))^n)/3.