A154949 Diagonal sums of Riordan array A154948.

1, 1, 3, 5, 10, 18, 34, 62, 115, 211, 389, 715, 1316, 2420, 4452, 8188, 15061, 27701, 50951, 93713, 172366, 317030, 583110, 1072506, 1972647, 3628263, 6673417, 12274327, 22576008, 41523752, 76374088, 140473848, 258371689, 475219625

Offset: 0

Author

Paul Barry, Jan 17 2009

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1,-1)

Programs

Mathematica

a=0; b=0; c=0; lst={}; Do[z=a+b+c+1; AppendTo[lst,z]; a=b; b=c; c=z; z=a+b+c; AppendTo[lst,z]; a=b; b=c; c=z,{n,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 17 2010 *)
LinearRecurrence[{1,2,0,-1,-1},{1,1,3,5,10},40] (* Harvey P. Dale, Nov 13 2022 *)

Formula

G.f.: 1/((1-x^2)(1 - x - x^2 - x^3)).

a(n) = sum{k=0..floor(n/2), sum{j=0..n-k+1, C(n-k+1-j,k+1)C(k-1,j)}}.

a(n) = -A000035(n)/2 + A001590(n+4)/2. - R. J. Mathar, Oct 25 2012