A046726 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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, 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