OFFSET
0,3
COMMENTS
FORMULA
G.f.=[1-z-sqrt(1-2z-3z^2-4tz^3+4z^3)]/[2(1-z+tz)z^2].
EXAMPLE
T(4,1)=3 because we have H(UH)D, (UH)DH and (UH)HD, where U=(1,1), H=(1,0), D=(1,-1) (the UH's are shown between parentheses).
Triangle begins:
1;
1;
2;
3,1;
6,3;
11,10;
23,26,2;
47,70,10;
MAPLE
G:=(1-z-sqrt(1-2*z-3*z^2-4*z^3*t+4*z^3))/2/z^2/(1-z+t*z): Gser:=simplify(series(G, z=0, 20)): P[0]:=1: for n from 1 to 16 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 16 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