%I #29 Jul 15 2019 04:58:52

%S 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,

%T 66,1,7,32,104,254,430,428,174,1,8,41,152,438,956,1454,1308,504,1,9,

%U 51,211,690,1796,3584,4976,4072,1406,1,10,62,282,1023,3028,7238,13256,16880,12796,4210

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

%C Rows are in order of decreasing number of components. Diagonals give number of semi-meanders with k components. - _Andrew Howroyd_, Nov 27 2015

%H Andrew Howroyd, <a href="/A046726/b046726.txt">Table of n, a(n) for n = 1..820</a>

%H P. Di Francesco, O. Golinelli, and E. Guitter, <a href="https://arxiv.org/abs/hep-th/9506030">Meander, folding and arch statistics</a>, arXiv:hep-th/9506030, 1995.

%H P. Di Francesco, O. Golinelli, and E. Guitter, <a href="https://doi.org/10.1016/S0895-7177(97)00202-1">Meander, folding and arch statistics</a>, Mathematical and Computer Modelling 26 (1997), 97-147.

%e Triangle starts:

%e 1;

%e 1, 1;

%e 1, 2, 2;

%e 1, 3, 6, 4;

%e 1, 4, 11, 16, 10;

%e 1, 5, 17, 37, 48, 24;

%e 1, 6, 24, 66, 126, 140, 66;

%e 1, 7, 32, 104, 254, 430, 428, 174;

%e 1, 8, 41, 152, 438, 956, 1454, 1308, 504;

%e ...

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

%K nonn,tabl

%O 1,5

%A _N. J. A. Sloane_

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

%E T(12,k)-T(40,k) from _Andrew Howroyd_, Dec 07 2015