A104544 Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k HH's, where H=(1,0).

1, 1, 1, 3, 0, 1, 5, 3, 0, 1, 11, 6, 3, 0, 1, 25, 13, 9, 3, 0, 1, 55, 40, 16, 12, 3, 0, 1, 129, 95, 60, 20, 15, 3, 0, 1, 303, 250, 155, 80, 25, 18, 3, 0, 1, 721, 661, 415, 235, 100, 31, 21, 3, 0, 1, 1743, 1708, 1206, 620, 335, 120, 38, 24, 3, 0, 1, 4241, 4515, 3262, 1946, 875, 455

Offset: 1

Author

Emeric Deutsch, Mar 14 2005

Keywords

• nonn
• tabl

Examples

			Triangle starts:
1;
1,1;
3,0,1;
5,3,0,1;
11,6,3,0,1;
T(4,1)=3 because we have HHUD, UDHH and UHHD, where U=(1,1), D=(1,-1) and H=(1,0).
		

Crossrefs

Column 0 yields A104545. Row sums yield the Motzkin numbers (A001006).

Formula

G.f.=G=G(t, z) satisfies z^2(1+z-tz)G^2-(1-tz)G+1+z-tz=0.