A026615 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(n,1)=T(n,n-1)=2n-1 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, 5, 5, 1, 1, 7, 10, 7, 1, 1, 9, 17, 17, 9, 1, 1, 11, 26, 34, 26, 11, 1, 1, 13, 37, 60, 60, 37, 13, 1, 1, 15, 50, 97, 120, 97, 50, 15, 1, 1, 17, 65, 147, 217, 217, 147, 65, 17, 1, 1, 19, 82, 212, 364, 434, 364, 212, 82, 19, 1, 1, 21

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 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 for j=0, i >= 0.

Crossrefs

Sequence in context: A130154 A208328 A134398 * A026681 A109128 A113245

Adjacent sequences: A026612 A026613 A026614 * A026616 A026617 A026618

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved