A067640 Table T(n,k) giving number of two-legged knot diagrams with n >= 0 self-intersections and k >= 0 tangencies, read by antidiagonals.

1, 2, 2, 8, 20, 10, 42, 174, 210, 70, 260, 1504, 2992, 2352, 588, 1796, 13300, 37100, 47820, 27720, 5544, 13396, 120744, 433620, 784672, 742296, 339768, 56628, 105706, 1122198, 4928798, 11515714, 15294006, 11376554, 4294290

Offset: 0

Author

N. J. A. Sloane, Feb 05 2002

Keywords

• nonn
• tabl

Examples

			Table begins
     1      2      10        70        588         5544         56628 ...
     2     20     210      2352      27720       339768       4294290 ...
     8    174    2992     47820     742296     11376554     173401952 ...
    42   1504   37100    784672   15294006    283730240    5095814988 ...
   260  13300  433620  11515714  271846056   5947557516  123429078160 ...
  1796 120744 4928798 158295072 4403552940 111289501120 2626033507768 ...
  ...
		

Links

• J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Knots, arXiv:math-ph/0102015, 2001-2002.

Crossrefs

Columns give A054993, A067641, A067642, A067643, rows give A005568, A067636, A067637, A067638, A067639.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 08 2002