A100132 a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 2^(n-3k).

1, 2, 4, 8, 18, 44, 112, 288, 740, 1896, 4848, 12384, 31624, 80752, 206208, 526592, 1344784, 3434272, 8770368, 22397568, 57198368, 146071744, 373034240, 952645120, 2432840256, 6212924032, 15866403584, 40519208448, 103476899968

Offset: 0

Author

Paul Barry, Nov 06 2004

Keywords

• easy
• nonn

Comments

Binomial transform of 1,1,1,1,3,3,7,7,41,... (g.f. (1-x)(1+x)^2/(1-2x^2-x^4)).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2)

Crossrefs

Cf. A100131, A100133.

Programs

Mathematica

LinearRecurrence[{4,-4,0,2},{1,2,4,8},30] (* Harvey P. Dale, Jun 07 2016 *)

PARI

a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*2^(n-3*k)); \\ Michel Marcus, Oct 09 2021

Formula

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

a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3).

a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)2^(n-3k/2)(1+(-1)^k)/2. - Paul Barry, Jan 22 2005