OFFSET
1,9
COMMENTS
FORMULA
G.f.=2/[2-2tz-t^2+t^2*z+t^2*z^2+t^2*sqrt((1+z+z^2)(1-3z+z^2))]-1.
EXAMPLE
T(5,4)=3 because we have HU(H)DH, HHU(H)D and U(H)DHH, where U=(1,1), H=(1,0) and D=(1,-1) and the steps that do not touch the x-axis are shown between parentheses.
Triangle starts:
1;
0,1;
0,1,1;
0,1,2,1;
0,2,2,3,1;
0,4,4,4,4,1;
0,8,8,8,7,5,1;
MAPLE
G:=2/(2-2*t*z-t^2+t^2*z+t^2*z^2+t^2*sqrt((1+z+z^2)*(1-3*z+z^2)))-1: Gser:=simplify(series(G, z=0, 15)): for n from 1 to 13 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 1 to 13 do seq(coeff(P[n], t, j), j=1..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Feb 14 2007
STATUS
approved