OFFSET
0,4
COMMENTS
LINKS
Paul Barry, On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences, J. Int. Seq. (2023) Vol. 26, Art. 23.4.7.
FORMULA
G.f. G=G(t,z) satisfies G = 1 + tzG + z^2*G + z^2*G^2 (see explicit expression at the Maple program).
EXAMPLE
T(4,2)=9 because we have hhH, hhUD, hHh, hUDh, Hhh, UDhh, hUhD, UhDh and UhhD.
MAPLE
G:=((1-t*z-z^2-sqrt((1-2*z-t*z-z^2)*(1+2*z-t*z-z^2)))*1/2)/z^2: Gser:=simplify(series(G, z=0, 15)): for n from 0 to 11 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 11 do seq(coeff(P[n], t, j), j=0..n) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 26 2007
STATUS
approved