OFFSET
0,5
COMMENTS
Row sums are the Motzkin numbers (A001006).
FORMULA
G.f.=G=G(t, z) satisfies z^2*(1-z+z^2-tz^2)G^2-(1-z)(1-z+z^2-tz^2)G+1-z=0.
EXAMPLE
Triangle begins:
1;
1;
1,1;
2,2;
5,3,1;
12,6,3;
Row n has 1+floor(n/2) terms.
T(5,2)=3 counts H(UD)(UD), (UD)H(UD) and (UD)(UD)H, where U=(1,1), H=(1,0), D=(1,-1) (the peaks at odd height are shown between parentheses).
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 03 2004
STATUS
approved