OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
FORMULA
G.f.: G=G(t,z) is given by G = 1 + z*G + z^2*c*(t*(G-1-z*G) + 1 + z*G), where c = (1-sqrt(1-4*z^2))/(2*z^2).
EXAMPLE
T(5,1)=2 because we have HUDUD and UDUDH, where U=(1,1), D=(1,-1), H=(1,0).
Triangle starts:
1;
1;
2;
3;
5, 1;
8, 2;
14, 5, 1;
23, 10, 2;
41, 22, 6, 1;
...
MAPLE
G := (1+z^2*c-t*z^2*c)/(1-z-z^3*c-t*z^2*c*(1-z)): c := ((1-sqrt(1-4*z^2))*1/2)/z^2: Gser := simplify(series(G, z = 0, 20)): for n from 0 to 17 do P[n] := sort(coeff(Gser, z, n)) end do: 1; 1; for n from 2 to 17 do seq(coeff(P[n], t, k), k = 0 .. floor((1/2)*n)-1) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jun 02 2011
STATUS
approved