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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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: A157522 A059674 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

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Last modified August 21 12:01 EDT 2017. Contains 290864 sequences.