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

0,2

Links

Table of n, a(n) for n=0..34.

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

Example

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 ...
  ...

Crossrefs

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

Sequence in context: A169888 A168506 A208966 * A098277 A242658 A080040

Adjacent sequences: A067637 A067638 A067639 * A067641 A067642 A067643

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 05 2002

Extensions

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

Status

approved