A026659 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, if n is odd, then T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k is odd and <=[ n/2 ] or if k is even and >[ n/2 ]; in all other cases, T(n,k)=T(n-1,k-1)+T(n-1,k).

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 5, 8, 5, 1, 1, 7, 13, 13, 7, 1, 1, 8, 20, 26, 20, 8, 1, 1, 10, 28, 59, 59, 28, 10, 1, 1, 11, 38, 87, 118, 87, 38, 11, 1, 1, 13, 49, 153, 205, 205, 153, 49, 13, 1, 1, 14, 62, 202, 358, 410, 358, 202, 62, 14, 1, 1, 16

Offset

1,5

Links

Table of n, a(n) for n=1..68.

Formula

T(n, k) = number of paths from (0, 0) to (n-k, k) in 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) is of form (2i+2h+1, 2h) or (2h, 2i+2h+1) for i, h>=0.

Crossrefs

Sequence in context: A282494 A156609 A026637 * A026386 A147532 A283796

Adjacent sequences: A026656 A026657 A026658 * A026660 A026661 A026662

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved