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A047000
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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.
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10
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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
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0,8
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COMMENTS
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Touches here includes the case where a step touches the line at a midpoint.
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LINKS
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Table of n, a(n) for n=0..74.
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EXAMPLE
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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.
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PROG
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(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. */
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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Definition corrected by Franklin T. Adams-Watters, Mar 10 2011
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STATUS
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approved
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