OFFSET
1,5
COMMENTS
FORMULA
G.f.: G(t,z) = 1/(1-tz-tz^2-tz^3*g) - 1, where g = 1 + zg + z^2*g + z^3*g^2.
EXAMPLE
T(5,2)=4 because we have UD'UUDUDUDD', UUDD'UUDUDD', UUDUDD'UUDD', and UUDUDUDD'UD' (the return steps are marked).
Triangle starts:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
2, 4, 6, 4, 1;
4, 7, 10, 10, 5, 1;
MAPLE
g := ((1-z-z^2-sqrt(1-2*z-z^2-2*z^3+z^4))*1/2)/z^3: G := 1/(1-t*z-t*z^2-t*z^3*g)-1: Gser := simplify(series(G, z = 0, 16)): for n to 12 do P[n] := sort(coeff(Gser, z, n)) end do: for n to 12 do seq(coeff(P[n], t, j), j = 1 .. n) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Oct 11 2009
STATUS
approved