A047120 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 touches the line y=x/4 only at lattice points.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 4, 2, 1, 1, 5, 10, 10, 6, 3, 1, 1, 6, 15, 20, 16, 6, 4, 1, 1, 7, 21, 35, 36, 22, 6, 5, 1, 1, 8, 28, 56, 71, 58, 28, 6, 6, 1, 1, 9, 36, 84, 127, 129, 86, 34, 12, 7, 1, 1, 10, 45, 120, 211, 256, 215, 120, 46, 19, 8, 1

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Crossrefs

Cf. A047089 (with y=x/2), A047100 (with y=x/3).

Programs

Mathematica

T[, 0] = 1; T[0, ] = 1; T[h_, k_] := T[h, k] = If[k-1 >= h/4 || k <= h/4, T[h, k-1], 0] + T[h-1, k];
Table[T[h - k, k], {h, 0, 11}, {k, h, 0, -1}]  // Flatten (* Jean-François Alcover, Mar 06 2019 *)