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

Author

N. J. A. Sloane

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
  ...
		

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.

Crossrefs

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

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