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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. 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 (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
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
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Definition corrected by Franklin T. Adams-Watters, Mar 10 2011
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)