OFFSET
0,3
COMMENTS
LINKS
Emeric Deutsch, Problem 10658: Another Type of Lattice Path, American Math. Monthly, 107, 2000, 368-370.
FORMULA
G.f. =(1-z)/[1+z-2tz-z(1-z)A(1+A)], where A=1+zA^2+zA^3=(2/3)*sqrt((z+3)/z)*sin((1/3)*arcsin(sqrt(z)*(z+18)/(z+3)^(3/2)))-1/3 (the g.f. of A027307).
EXAMPLE
T(2,1)=2 because we have uudd and UUdddd.
Triangle begins:
1;
0,2;
4,2,4;
32,18,8,8;
252,146,60,24,16;
MAPLE
A:=(2/3)*sqrt((z+3)/z)*sin((1/3)*arcsin(sqrt(z)*(z+18)/(z+3)^(3/2)))-1/3: G:=(1-z)/(1+z-2*t*z-z*(1-z)*A*(1+A)): Gser:=simplify(series(G, z=0, 12)): P[0]:=1: for n from 1 to 9 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 9 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jun 11 2005
STATUS
approved