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 A026714 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k=[ (n-1)/2 ] or k=[ n/2 ] or k=[ (n+2)/2 ], else T(n,k)=T(n-1,k-1)+T(n-1,k). 10

%I

%S 1,1,1,1,3,1,1,5,5,1,1,7,13,7,1,1,8,25,25,8,1,1,9,40,63,40,9,1,1,10,

%T 49,128,128,49,10,1,1,11,59,217,319,217,59,11,1,1,12,70,276,664,664,

%U 276,70,12,1,1,13,82,346,1157,1647,1157,346,82,13

%N Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k=[ (n-1)/2 ] or k=[ n/2 ] or k=[ (n+2)/2 ], else T(n,k)=T(n-1,k-1)+T(n-1,k).

%F T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) if |i-j|<=2.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_

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