OFFSET
0,4
LINKS
D. Baccherini, D. Merlini and R. Sprugnoli, Level generating trees and proper Riordan arrays, Applicable Analysis and Discrete Mathematics, 2, 2008, 69-91 (see p. 88). [From Emeric Deutsch, Sep 21 2008]
FORMULA
G.f.: (1-q)/(z(1+z)(2-t+tq)), where q = sqrt(1 - 4z - 4z^2). - Emeric Deutsch, Jun 06 2005
T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n,k+1), T(0,0)=1. - Philippe Deléham, Nov 18 2009
EXAMPLE
Triangle begins:
1;
1, 1;
3, 3, 1;
9, 9, 5, 1;
31, 31, 19, 7, 1;
...
MAPLE
q:=sqrt(1-4*z-4*z^2): G:=(1-q)/z/(1+z)/(2-t+t*q): Gser:=simplify(series(G, z=0, 13)): P[0]:=1: for n from 1 to 10 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 10 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form - Emeric Deutsch, Jun 06 2005
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jun 05 2005
EXTENSIONS
More terms from Emeric Deutsch, Jun 06 2005
STATUS
approved