A101551 a(n) = C(n-2,2)+C(n-5,5)+...+C(n-(3*floor((n-3)/3)+2),3*floor((n-3)/3)+2).

0, 0, 0, 0, 1, 3, 6, 10, 15, 21, 29, 42, 66, 111, 192, 330, 554, 906, 1452, 2303, 3651, 5826, 9382, 15225, 24807, 40431, 65748, 106584, 172321, 278184, 448980, 725140, 1172412, 1897380, 3072365, 4975551, 8055918, 13038606, 21096027, 34125561

Offset: 0

Author

Paul Barry, Dec 06 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 (3,-3,1,0,0,1)

Crossrefs

Cf. A024490, A101552.

Programs

Mathematica

CoefficientList[Series[x^4/((1-x)^3-x^6),{x,0,50}],x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3,-3,1,0,0,1},{0,0,0,0,1,3},40] (* Harvey P. Dale, Feb 20 2014 *)

Formula

G.f.: x^4/((1-x)^3-x^6) = -x^4/ ((x^2+x-1)*(x^4-x^3+2*x^2-2*x+1)).

a(n) = Sum_{k=0..n} if(mod(k+1, 3)=0, C(n-k, k), 0).

a(n+2) = Sum_{k=0..floor(n/6)} binomial(n-3k, 3k+2). - Paul Barry, Jan 13 2005