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

0,13

Links

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

Example

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

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 *)

Crossrefs

Cf. A048116.

Sequence in context: A093569 A073091 A125250 * A028961 A373242 A110177

Adjacent sequences: A048110 A048111 A048112 * A048114 A048115 A048116

Keyword

nonn,tabl,walk

Author

Clark Kimberling

Extensions

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

Status

approved