cp's OEIS Frontend

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.

%I A047000 #11 Jun 13 2017 02:16:50
%S A047000 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 A047000 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 A047000 83,30,12,18,7,1,1,10,44,112,180,186,113,30,30
%N 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.
%C A047000 Touches here includes the case where a step touches the line at a midpoint.
%e A047000 Diagonals (starting on row #0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,2,1,1}; ...
%e A047000 T(2,3) = 5; the 5 allowed paths to (2,3) are UUURR, UURUR, UURRU, URUUR, and URURU.
%o A047000 (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 A047000 The sequence T(2n, n)/2 for n=1, 2, 3, ... is A006013.
%K A047000 nonn,tabl
%O A047000 0,8
%A A047000 _Clark Kimberling_
%E A047000 Definition corrected by _Franklin T. Adams-Watters_, Mar 10 2011