A085278 Expansion of (1+2x)^2/((1-x^2)(1-2x)).

1, 6, 17, 38, 81, 166, 337, 678, 1361, 2726, 5457, 10918, 21841, 43686, 87377, 174758, 349521, 699046, 1398097, 2796198, 5592401, 11184806, 22369617, 44739238, 89478481, 178956966, 357913937, 715827878, 1431655761, 2863311526

Offset: 0

Author

Paul Barry, Jun 25 2003

Keywords

• easy
• nonn

Comments

Binomial transform is A085277.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Programs

Mathematica

CoefficientList[Series[(1+2x)^2/((1-x^2)(1-2x)),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-2},{1,6,17},40] (* Harvey P. Dale, Sep 19 2016 *)

Formula

a(n)=16*2^n/3+(-1)^n/6-9/2.

G.f.: (2*x+1)^2 / ( (x-1)*(2*x-1)*(1+x) ). - R. J. Mathar, Nov 20 2014

Extensions

Missing parenthesis in definition corrected by Harvey P. Dale, Sep 19 2016