A099560 a(n) = Sum_{k=0..floor(n/3)} C(n-2k,k-1).

0, 0, 0, 1, 1, 1, 3, 4, 5, 9, 13, 18, 28, 41, 59, 88, 129, 188, 277, 406, 594, 872, 1278, 1872, 2745, 4023, 5895, 8641, 12664, 18559, 27201, 39865, 58424, 85626, 125491, 183915, 269542, 395033, 578948, 848491, 1243524, 1822472, 2670964, 3914488

Offset: 0

Author

Paul Barry, Oct 22 2004

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A074331, A099561, A099562.

Programs

Mathematica

Table[Sum[Binomial[n-2k,k-1],{k,0,Floor[n/3]}],{n,0,50}] (* or *) LinearRecurrence[{1,0,2,-1,0,-1},{0,0,0,1,1,1},50] (* Harvey P. Dale, May 25 2014 *)
CoefficientList[Series[x^3/((1 - x^3) (1 - x - x^3)), {x,0,50}], x] (* G. C. Greubel, Apr 28 2017 *)

PARI

x='x+O('x^50); concat([0,0,0], Vec(x^3/((1-x^3)*(1-x-x^3)))) \\ G. C. Greubel, Apr 28 2017

Formula

G.f.: x^3/((1-x^3)(1-x-x^3)).

a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-6).

a(n) = a(n-3) + A000930(n-3). - R. J. Mathar, Nov 24 2013

a(n) = A000930(n-2) - A079978(n+1), n>3. - R. J. Mathar, Dec 08 2022