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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=2x unless x=0 or x=h.
0

%I #10 May 11 2021 21:32:45

%S 1,1,1,1,1,1,1,2,2,1,1,1,2,3,1,1,2,2,5,4,1,1,3,4,7,9,5,1,1,4,3,7,16,

%T 14,6,1,1,5,7,7,23,30,20,7,1,1,6,12,14,30,53,50,27,8,1,1,7,18,12,30,

%U 83,103,77,35,9,1,1,8,25,30,30,113,186,180,112,44

%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=2x unless x=0 or x=h.

%e Diagonals (beginning on row 0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,1,2,3,1}; ...

%Y Cf. A047000 (mirror image).

%K nonn,tabl

%O 0,8

%A _Clark Kimberling_

%E a(0) = 1 inserted by _Sean A. Irvine_, May 11 2021