A062038 Triangular array T(n,k) giving number of alternating link diagrams with n >= 0 crossings, k = 0..[n/2] connected components and two external legs.

1, 2, 8, 1, 42, 12, 260, 114, 4, 1796, 1030, 90, 13396, 9290, 1349, 22, 105706, 84840, 17220, 728, 870772, 787082, 203568, 14884, 140, 7420836, 7415814, 2312094, 244908, 6120, 65004584, 70867212, 25691670, 3575045, 158354, 969

Offset

0,2

Comments

Rows have lengths 1,1,2,2,3,3,4,4,...

Links

Table of n, a(n) for n=0..35.

J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Colored Links, J. Knot Theory, 10 (2001), 1233-1267.

Example

1; 2; 8,1; 42,12; 260,114,4; 1796,1030,90; ...

Crossrefs

Columns give A054993, A062386, A067767, A067768.

Sequence in context: A165274 A221074 A065249 * A318106 A308036 A305677

Adjacent sequences: A062035 A062036 A062037 * A062039 A062040 A062041

Keyword

nonn,tabf

Author

N. J. A. Sloane, Feb 09 2002

Status

approved