A046726 Triangle of numbers of semi-meanders of order n with k components.

1, 1, 1, 1, 2, 2, 1, 3, 6, 4, 1, 4, 11, 16, 10, 1, 5, 17, 37, 48, 24, 1, 6, 24, 66, 126, 140, 66, 1, 7, 32, 104, 254, 430, 428, 174, 1, 8, 41, 152, 438, 956, 1454, 1308, 504, 1, 9, 51, 211, 690, 1796, 3584, 4976, 4072, 1406, 1, 10, 62, 282, 1023, 3028, 7238, 13256, 16880, 12796, 4210

Offset

1,5

Comments

Rows are in order of decreasing number of components. Diagonals give number of semi-meanders with k components. - Andrew Howroyd, Nov 27 2015

Links

Andrew Howroyd, Table of n, a(n) for n = 1..820

P. Di Francesco, O. Golinelli, and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.

P. Di Francesco, O. Golinelli, and E. Guitter, Meander, folding and arch statistics, Mathematical and Computer Modelling 26 (1997), 97-147.

Example

Triangle starts:
  1;
  1, 1;
  1, 2,  2;
  1, 3,  6,   4;
  1, 4, 11,  16,  10;
  1, 5, 17,  37,  48,  24;
  1, 6, 24,  66, 126, 140,   66;
  1, 7, 32, 104, 254, 430,  428,  174;
  1, 8, 41, 152, 438, 956, 1454, 1308, 504;
  ...

Crossrefs

Diagonals include A000682, A046721, A046722, A046723, A046724, A046725. Columns include A000027, A046691. Row sums are in A000108 (Catalan numbers).

Sequence in context: A107230 A159830 A293472 * A082137 A091187 A318607

Adjacent sequences: A046723 A046724 A046725 * A046727 A046728 A046729

Keyword

nonn,tabl

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 05 2000

T(12,k)-T(40,k) from Andrew Howroyd, Dec 07 2015

Status

approved