A047070 Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=2x unless x=0 or x=h.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 2, 5, 4, 1, 1, 3, 4, 7, 9, 5, 1, 1, 4, 3, 7, 16, 14, 6, 1, 1, 5, 7, 7, 23, 30, 20, 7, 1, 1, 6, 12, 14, 30, 53, 50, 27, 8, 1, 1, 7, 18, 12, 30, 83, 103, 77, 35, 9, 1, 1, 8, 25, 30, 30, 113, 186, 180, 112, 44

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Diagonals (beginning on row 0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,1,2,3,1}; ...
		

Crossrefs

Cf. A047000 (mirror image).

Extensions

a(0) = 1 inserted by Sean A. Irvine, May 11 2021