OFFSET
0,3
COMMENTS
FORMULA
G.f.=2/[1-z-2tz^3+2z^3+sqrt(1-2z-3z^2)].
EXAMPLE
T(7,2)=3 because we have (UDH)(UDH)H, H(UDH)(UDH) and (UDH)H(UDH), where U=(1,1),H=(1,0),D=(1,-1) (the UDH's starting at level 0 are shown between parentheses).
Triangle starts:
1;
1;
2;
3,1;
7,2;
16,5;
40,10,1;
MAPLE
G:=2/(1-z-2*t*z^3+2*z^3+sqrt(1-2*z-3*z^2)): Gser:=simplify(series(G, z=0, 21)): P[0]:=1: for n from 1 to 17 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 17 do seq(coeff(t*P[n], t^j), j=1..1+floor(n/3)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 09 2005
STATUS
approved