A026626 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(n,1)=T(n,n-1)=[ 3n/2 ] for n >= 1; T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=k<=n-2, n >= 4.

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 8, 6, 1, 1, 7, 14, 14, 7, 1, 1, 9, 21, 28, 21, 9, 1, 1, 10, 30, 49, 49, 30, 10, 1, 1, 12, 40, 79, 98, 79, 40, 12, 1, 1, 13, 52, 119, 177, 177, 119, 52, 13, 1, 1, 15, 65, 171, 296, 354, 296, 171, 65, 15, 1, 1, 16, 80

Offset

1,5

Links

Table of n, a(n) for n=1..69.

Index entries for sequences related to rooted trees

Formula

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 and even and for j=0, i >= 0 and even.

Example

1;
1, 1;
1, 3, 1;
1, 4, 4, 1;
1, 6, 8, 6, 1;
1, 7, 14, 14, 7, 1;
1, 9, 21, 28, 21, 9, 1;
1, 10, 30, 49, 49, 30, 10, 1;
1, 12, 40, 79, 98, 79, 40, 12, 1;
1, 13, 52, 119, 177, 177, 119, 52, 13, 1;
1, 15, 65, 171, 296, 354, 296, 171, 65, 15, 1;

Crossrefs

Sequence in context: A026670 A131402 A238498 * A136482 A026648 A026747

Adjacent sequences: A026623 A026624 A026625 * A026627 A026628 A026629

Keyword

nonn,tabl,easy

Author

Clark Kimberling

Status

approved