login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A098576 a(n) = Sum_{k=0..floor(n/4)} C(n-2*k,2*k) * 3^k. 4

%I #16 Sep 08 2022 08:45:15

%S 1,1,1,1,4,10,19,31,55,109,220,424,793,1489,2845,5473,10480,19954,

%T 37963,72391,138259,263989,503608,960400,1831969,3495505,6669865,

%U 12725425,24276892,46314874,88362451,168586303,321640831,613639981,1170726484

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

%H G. C. Greubel, <a href="/A098576/b098576.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,3).

%F G.f.: (1-x)/((1-x)^2-3*x^4).

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

%t Table[Sum[Binomial[n-2k,2k]3^k,{k,0,Floor[n/4]}],{n,0,40}] (* or *) LinearRecurrence[{2,-1,0,3},{1,1,1,1},40] (* _Harvey P. Dale_, Dec 04 2011 *)

%o (PARI) x='x+O('x^30); Vec((1-x)/((1-x)^2-3*x^4)) \\ _G. C. Greubel_, Feb 03 2018

%o (Magma) I:=[1,1,1,1]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) + 3*Self(n-4): n in [1..30]]; // _G. C. Greubel_, Feb 03 2018

%Y Cf. A097116, A098575.

%K easy,nonn

%O 0,5

%A _Paul Barry_, Sep 16 2004

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)