OFFSET
0,3
COMMENTS
FORMULA
G.f.: G(t,z) = 2/(1-z-t*z+(1-z+t*z)*sqrt(1-4*z^2)).
EXAMPLE
T(7,2)=3 because we have HHUDHUD, HUDHHUD, and HUDHUDH, where U=(1,1), D=(1,-1), H=(1,0).
Triangle starts:
1;
1;
2;
2, 1;
4, 2;
4, 6;
9, 10, 1;
9, 23, 3;
23, 36, 11;
MAPLE
G := 2/(1-z-t*z+(1-z+t*z)*sqrt(1-4*z^2)): Gser := simplify(series(G, z = 0, 20)): for n from 0 to 18 do P[n] := sort(expand(coeff(Gser, z, n))) end do: for n from 0 to 18 do seq(coeff(P[n], t, k), k = 0 .. floor((1/3)*n)) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jun 01 2011
STATUS
approved