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%I #9 Mar 30 2012 18:56:09
%S 1,1,1,1,3,1,1,4,4,1,1,6,8,6,1,1,7,14,14,7,1,1,9,21,36,21,9,1,1,10,30,
%T 57,57,30,10,1,1,12,40,108,114,108,40,12,1,1,13,52,148,222,222,148,52,
%U 13,1,1,15,65,240,370,558,370,240,65,15,1,1,16
%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 n is even and k is odd, 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) for i=0, j >= 0 if both i and j are even.
%F Equals 2*A007318 - A034851 (i.e. twice Pascal's triangle - the Losanitch triangle). - _Gary W. Adamson_, Dec 31 2007
%Y Cf. A007318, A034851.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_
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