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

0,2

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).

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

Mathematica

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

Prog

(PARI) a(n)=3*(0^n/3+2^n+n<<n)/4 \\ Charles R Greathouse IV, Nov 11 2011
(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

Crossrefs

Sequence in context: A034330 A264685 A320731 * A228820 A335470 A003262

Adjacent sequences: A084855 A084856 A084857 * A084859 A084860 A084861

Keyword

easy,nonn

Author

Paul Barry, Jun 11 2003

Status

approved