A084858 Binomial transform of A001651.

1, 3, 9, 24, 60, 144, 336, 768, 1728, 3840, 8448, 18432, 39936, 86016, 184320, 393216, 835584, 1769472, 3735552, 7864320, 16515072, 34603008, 72351744, 150994944, 314572800, 654311424, 1358954496, 2818572288, 5838471168, 12079595520

Offset: 0

Author

Paul Barry, Jun 11 2003

Keywords

• easy
• nonn

Comments

a(n+1)/3 = A001792(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Programs

Magma

I:=[1, 3, 9]; [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jun 24 2012

Mathematica

CoefficientList[Series[(x^2-x+1)/(1-2x)^2,{x,0,40}],x] (* Vincenzo Librandi, Jun 24 2012 *)

PARI

a(n)=3*(0^n/3+2^n+n<Charles R Greathouse IV, Nov 11 2011

Formula

G.f.: (x^2 - x + 1)/(1-2*x)^2.

a(n) = 3*(0^n/3 + 2^n + n*2^n)/4.

For n > 1: a(n) = 2*a(n-1) + 3*2^(n-2). - Philippe Deléham, Nov 10 2011

a(n) = 4*a(n-1) - 4*a(n-2). - Vincenzo Librandi, Jun 24 2012