OFFSET
0,3
COMMENTS
FORMULA
G.f. G=G(t, z) satisfies (1-t)z^5*G^5-(1-t)z^4*G^4+zG^2-G+1=0.
EXAMPLE
T(5,1)=5 because we have UDUUUUDDDD, UUUDDDDUD, UUUUDDDUDD, UUUUDDUDDD and UUUUDUDDDD, where U=(1,1), D=(1,-1).
Triangle starts:
1;
1;
2;
5;
13,1;
37,5;
111,21;
345,84;
1104,322,4;
3611,1215,36;
MAPLE
Order:=20: Y:=solve(series((Y-Y^2)/(1-(1-t)*Y^4+(1-t)*Y^5), Y)=z, Y): 1; for n from 1 to 17 do seq(coeff(t*coeff(Y, z^(n+1)), t^j), j=1..1+floor(n/4)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 03 2005
STATUS
approved