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

0,8

Links

Table of n, a(n) for n=0..77.

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 *)

Crossrefs

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

Sequence in context: A208891 A177767 A047030 * A096751 A293551 A099233

Adjacent sequences: A047117 A047118 A047119 * A047121 A047122 A047123

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved