A154949 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..33.

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

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

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 *)

CROSSREFS

Sequence in context: A010049 A356507 A094986 * A318248 A107232 A134522

Adjacent sequences: A154946 A154947 A154948 * A154950 A154951 A154952

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 17 2009

STATUS

approved