A048113 Triangular array T read by rows: T(h,k) = number of paths consisting of steps from (1,1) to (h,k) such that each step has length 1 directed up or right and each vertex (i,j) satisfies i/2<=j<=2i, for h=0,1,2,... and k=0,1,2,...

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 12, 6, 0, 0, 0, 0, 0, 0, 6, 18, 18, 6, 0, 0, 0, 0, 0, 0, 0, 24, 36, 24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 60, 60, 24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 84, 120, 84, 24, 0, 0, 0, 0

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl
• walk

Examples

			Rows: {0}; {0,0}; {0,1,0}; {0,1,1,0}; ...
		

Links

• Alois P. Heinz, Rows n = 0..200, flattened

Crossrefs

Cf. A048116.

Programs

Mathematica

T[0, 0] = T[0, 1] = T[1, 0] = 0; T[1, 1] = T[2, 1] = T[1, 2] = 1; T[h_, k_] /; Not[h/2 <= k <= 2h] = 0; T[h_, k_] := T[h, k] = If[h-1 >= k/2, T[h-1, k], 0] + If[k-1 >= h/2, T[h, k-1], 0]; row[s_] := Table[T[h, s-h], {h, 0, s}]; Table[row[s], {s, 0, 12}] // Flatten (* Jean-François Alcover, Dec 02 2016 *)

Extensions

Offset changed to 0 by Alois P. Heinz, Oct 06 2016