A108485 Sum binomial(2n-2k,2k)2^(n-k), k=0..floor(n/2).

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

Offset

0,2

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).

Formula

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A196010 A121071 A092199 * A371482 A018940 A271958

Adjacent sequences: A108482 A108483 A108484 * A108486 A108487 A108488

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved