%I A027144
%S A027144 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,
%T A027144 72,64,32,1,14,42,152,152,288,96,128,1,16,56,224,304,512,384,
%U A027144 256,128,1,18,72,352,528,1344,896,1536,384,512,1,20,90,480,880
%N A027144 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 A027144 1; 1,2; 1,4,2; 1,6,6,8; 1,8,12,16,8; ...
%Y A027144 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.
%Y A027144 Sequence in context: A124927 A126279 A135837 this_sequence A158303 A035607 
               A059370
%Y A027144 Adjacent sequences: A027141 A027142 A027143 this_sequence A027145 A027146 
               A027147
%K A027144 nonn,tabl
%O A027144 1,3
%A A027144 Clark Kimberling (ck6(AT)evansville.edu)