A108485 a(n) = Sum_{k=0..floor(n/2)} binomial(2n-2k,2k)2^(n-k).

1, 2, 6, 32, 140, 600, 2632, 11520, 50320, 219936, 961376, 4201984, 18366144, 80275840, 350873728, 1533616128, 6703206656, 29298713088, 128060286464, 559732334592, 2446506216448, 10693312305152, 46738866751488

Offset: 0

Author

Paul Barry, Jun 04 2005

Keywords

• easy
• nonn

Comments

In general, Sum_{k=0..floor(n/2)} C(2n-2k,2k)a^k*b^(n-k) has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,8,-4).

Programs

Magma

I:=[1, 2, 6, 32]; [n le 4 select I[n] else 4*Self(n-1)+8*Self(n-3)-4*Self(n-4): n in [1..30]]; // Vincenzo Librandi. Jun 26 2012

Mathematica

LinearRecurrence[{4,0,8,-4},{1,2,6,32},40] (* or *) CoefficientList[Series[(1-2x-2x^2)/(1-4x-8x^3+4x^4),{x,0,40}],x] (* Vincenzo Librandi, Jun 26 2012 *)

Formula

G.f.: (1-2x-2x^2)/(1-4x-8x^3+4x^4).

a(n) = 4a(n-1)+8a(n-3)-4a(n-4).