

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.


10



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
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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(h1, k)*(h1!=2*k)+T(h, k1)*(h!=2*k2 && h!=2*k1)) /* Inefficient. */


CROSSREFS

The sequence T(2n, n)/2 for n=1, 2, 3, ... is A006013.
Sequence in context: A059674 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. AdamsWatters, Mar 10 2011


STATUS

approved



