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%I #6 Mar 30 2012 18:56:14
%S 1,1,2,1,4,2,1,6,6,8,1,8,12,16,8,1,10,20,48,24,32,1,12,30,80,72,64,32,
%T 1,14,42,152,152,288,96,128,1,16,56,224,304,512,384,256,128,1,18,72,
%U 352,528,1344,896,1536,384,512,1,20,90,480,880
%N Triangular array T given by rows: T(n,0)=1 for n >= 0, T(1,1)=2; for even n >= 2, T(n,k)=T(n-2,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-1 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-2, T(n,n)=T(n-1,n-1); for odd n<=3, T(n,k)=T(n,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-2 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-1, T(n,n)=T(n-1,n-1)+T(n,n-1).
%e 1; 1,2; 1,4,2; 1,6,6,8; 1,8,12,16,8; ...
%Y T(n, k) = number of paths from (0, 0) to (n, n-k) in the directed graph having vertices (i, j) for i >= 0, j >= 0 and edges as follows: for i >= 0, j >= 0, the unit square ABCD labeled counterclockwise from vertex A=(i, j) has directed edges AB, DC, AD, BC and also AC and DB if i and j are both even.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_
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