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).

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, 1, 14, 42, 152, 152, 288, 96, 128, 1, 16, 56, 224, 304, 512, 384, 256, 128, 1, 18, 72, 352, 528, 1344, 896, 1536, 384, 512, 1, 20, 90, 480, 880

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			1; 1,2; 1,4,2; 1,6,6,8; 1,8,12,16,8; ...
		

Crossrefs

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.