A127832 Array T by antidiagonals: for h>=0 and k>=0, T(h,k)=number of UR paths from (0,0) to (h,k) that touch the line y=2x/3 only at lattice points. A UR path is a path of steps of length 1 each directed up or right.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 4, 5, 4, 3, 1, 1, 5, 9, 9, 7, 4, 1, 1, 6, 14, 18, 9, 11, 5, 1, 1, 7, 20, 32, 27, 11, 16, 6, 1, 1, 8, 27, 52, 59, 27, 27, 22, 7, 1, 1, 9, 35, 79, 111, 86, 54, 49, 29, 8, 1, 1, 10, 44, 114, 190, 197, 140, 103, 78, 37, 9, 1, 1, 11, 54, 158, 304, 387

Offset: 1

Author

Clark Kimberling, Feb 01 2007

Keywords

• nonn
• tabl

Examples

			Northwest corner:
0 1 1 1 1 1
1 1 2 3 4 5
1 1 2 5 9 14
1 2 4 9 18 32
1 3 7 9 27 59
The 4 UR paths for T(3,2) are RRRUU, RRURU, UURRR, URURR. These
paths touch the line y=2x/3 only at the lattice points (0,0) and (3,2).
		

Crossrefs

Cf. A047110, A127833.