A098575 a(n) = Sum_{k=0..floor(n/4)} C(n-2*k,2*k)*2^k.

1, 1, 1, 1, 3, 7, 13, 21, 35, 63, 117, 213, 379, 671, 1197, 2149, 3859, 6911, 12357, 22101, 39563, 70847, 126845, 227045, 406371, 727391, 1302101, 2330901, 4172443, 7468767, 13369293, 23931621, 42838835, 76683583, 137266917, 245713493

Offset: 0

Author

Paul Barry, Sep 16 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2).

Crossrefs

Cf. A007909, A098576.

Programs

Magma

I:=[1, 1, 1, 1]; [n le 4 select I[n] else 2*Self(n-1)-Self(n-2)+2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

Mathematica

CoefficientList[Series[(1-x)/((1-x)^2-2x^4),{x,0,40}],x] (* Vincenzo Librandi, Jun 17 2012 *)

PARI

x='x+O('x^30); Vec((1-x)/((1-x)^2-2*x^4)) \\ G. C. Greubel, Feb 03 2018

Formula

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

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