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%I #11 Jun 13 2017 02:16:50
%S 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,
%T 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,
%U 83,30,12,18,7,1,1,10,44,112,180,186,113,30,30
%N 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.
%C Touches here includes the case where a step touches the line at a midpoint.
%e Diagonals (starting on row #0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,2,1,1}; ...
%e T(2,3) = 5; the 5 allowed paths to (2,3) are UUURR, UURUR, UURRU, URUUR, and URURU.
%o (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. */
%Y The sequence T(2n, n)/2 for n=1, 2, 3, ... is A006013.
%K nonn,tabl
%O 0,8
%A _Clark Kimberling_
%E Definition corrected by _Franklin T. Adams-Watters_, Mar 10 2011
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