A093834 Expansion of (1-2x)^2/((1-3x)(1-4x)).

1, 3, 13, 55, 229, 943, 3853, 15655, 63349, 255583, 1028893, 4135255, 16600069, 66577423, 266841133, 1068958855, 4280618389, 17136822463, 68590336573, 274490486455, 1098349366309, 4394559726703, 17581725691213, 70337363118055

Offset: 0

Author

Paul Barry, Apr 17 2004

Keywords

• easy
• nonn

Comments

Binomial transform of A093833.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-12).

Crossrefs

Cf. A085350.

Programs

Mathematica

CoefficientList[Series[(1-2x)^2/((1-3x)(1-4x)),{x,0,30}],x] (* or *) Join[{1},LinearRecurrence[{7,-12},{3,13},30]] (* Harvey P. Dale, Dec 27 2011 *)

Formula

a(n)=4^n-3^n/3-0^n/3. a(n+1)=4^(n+1)-3^n, n>0.

a(0)=1, a(1)=3, a(2)=13, a(n)=7*a(n-1)-12*a(n-2) [From Harvey P. Dale, Dec 27 2011]