A047000 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=x/2 except at the endpoints.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 4, 5, 2, 2, 1, 1, 5, 9, 7, 4, 3, 1, 1, 6, 14, 16, 7, 3, 4, 1, 1, 7, 20, 30, 23, 7, 7, 5, 1, 1, 8, 27, 50, 53, 30, 14, 12, 6, 1, 1, 9, 35, 77, 103, 83, 30, 12, 18, 7, 1, 1, 10, 44, 112, 180, 186, 113, 30, 30

Offset

0,8

Comments

Touches here includes the case where a step touches the line at a midpoint.

Links

Table of n, a(n) for n=0..74.

Example

Diagonals (starting on row #0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,2,1,1}; ...
T(2,3) = 5; the 5 allowed paths to (2,3) are UUURR, UURUR, UURRU, URUUR, and URURU.

Prog

(PARI) T(h, k)=if(h==0 || k==0, 1, T(h-1, k)*(h-1!=2*k)+T(h, k-1)*(h!=2*k-2 && h!=2*k-1)) /* Inefficient. */

Crossrefs

The sequence T(2n, n)/2 for n=1, 2, 3, ... is A006013.

Sequence in context: A367624 A342748 A117545 * A288915 A175062 A139767

Adjacent sequences: A046997 A046998 A046999 * A047001 A047002 A047003

Keyword

nonn,tabl

Author

Clark Kimberling

Extensions

Definition corrected by Franklin T. Adams-Watters, Mar 10 2011

Status

approved