cp's OEIS Frontend

A207851 Number of meanders of order 2n+1 (4*n+2 crossings of the infinite line) with only central 1-1 cut (no other 1-1 cuts).

%I A207851 #32 Jun 17 2019 02:51:45
%S A207851 4,16,324,12100,595984,35236096,2363709924,174221090404,
%T A207851 13815880848784,1161868621405636,102544273501721104,
%U A207851 9424551852935116804,896612457556434503824,87881363502264179831824,8840846163309028336017124
%N A207851 Number of meanders of order 2n+1 (4*n+2 crossings of the infinite line) with only central 1-1 cut (no other 1-1 cuts).
%C A207851 Central cut is a 1-1 cut at the center of the meander (the i-line is for i=n).
%D A207851 A. Panayotopoulos and P. Tsikouras, Properties of meanders, JCMCC 46 (2003), 181-190.
%D A207851 A. Panayotopoulos and P. Vlamos, Meandric Polygons, Ars Combinatoria 87 (2008), 147-159.
%H A207851 Panayotis Vlamos, <a href="/A207851/b207851.txt">Table of n, a(n) for n = 1..22</a>
%H A207851 Iwan Jensen, <a href="http://arxiv.org/abs/cond-mat/9910313">Enumeration of plane meanders</a>, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.
%H A207851 S. K. Lando and A. K. Zvonkin, <a href="http://dx.doi.org/10.1016/0304-3975(93)90316-L">Plane and projective meanders</a>, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.
%H A207851 A. Panayotopoulos and P. Tsikouras, <a href="https://msh.revues.org/2808">The multimatching property of nested sets</a>, Math. & Sci. Hum. 149 (2000), 23-30.
%H A207851 A. Panayotopoulos and P. Tsikouras, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Panayotopoulos/panayo4.html">Meanders and Motzkin Words</a>, J. Integer Seqs., Vol. 7, 2004.
%H A207851 A. Panayotopoulos and P. Vlamos, <a href="http://dx.doi.org/10.1007/978-3-642-33412-2_49">Cutting Degree of Meanders</a>, Artificial Intelligence Applications and Innovations, IFIP Advances in Information and Communication Technology, Volume 382, 2012, pp 480-489; DOI 10.1007/978-3-642-33412-2_49. - From _N. J. A. Sloane_, Dec 29 2012
%o A207851 (C/C++) int a(int n){
%o A207851       return w2(i)^2;
%o A207851 }
%o A207851 int w1(int order, int i){
%o A207851       if (i%2==0) error("error in w1(%d,%d), i is even\n",order,i);
%o A207851       if (order%2) error("error in w1(%d,%d), order is odd\n",order,i);
%o A207851       return w2(i+1)*w(order-i+1);
%o A207851 }
%o A207851 int w2(int order){
%o A207851       if (order%2) error("error in w2(%d), order is odd\n",order);
%o A207851       return w(order)-w3(order);
%o A207851 }
%o A207851 int w3(int order){
%o A207851       if (order%2) error("error in w3(%d), order is odd\n",order);
%o A207851       int sum=0;
%o A207851       int i;
%o A207851       for (i=3;i<=order-3;i+=2)
%o A207851           sum+=w1(order,i);
%o A207851       return sum;
%o A207851 }
%o A207851 // w(int i), no source here, is the respective meandric number according to Jensen A005315
%Y A207851 Cf. A005315, A192927.
%K A207851 nonn
%O A207851 1,1
%A A207851 _Panayotis Vlamos_ and _Antonios Panayotopoulos_, Feb 21 2012