OFFSET
0,4
COMMENTS
A Grand Motzkin path is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).
Row n contains 1 + floor(n/2) terms.
Row sums yield the central trinomial coefficients (A002426).
FORMULA
EXAMPLE
T(4,2)=4 because we have udud, dudu, uddu and duud, where u=(1,1), d=(1,-1), h=(1,0).
Triangle begins:
1;
1;
1, 2;
1, 6;
1, 14, 4;
1, 30, 20;
1, 64, 68, 8;
MAPLE
M:=(1-z-sqrt(1-2*z-3*z^2))/2/z^2: G:=1/(1-z-2*t*z^2*M): Gser:=simplify(series(G, z=0, 17)): P[0]:=1: for n from 1 to 14 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 14 do seq(coeff(t*P[n], t^k), k=1..1+floor(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jun 22 2005
STATUS
approved