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).

4, 16, 324, 12100, 595984, 35236096, 2363709924, 174221090404, 13815880848784, 1161868621405636, 102544273501721104, 9424551852935116804, 896612457556434503824, 87881363502264179831824, 8840846163309028336017124

Offset

1,1

Comments

Central cut is a 1-1 cut at the center of the meander (the i-line is for i=n).

References

A. Panayotopoulos and P. Tsikouras, Properties of meanders, JCMCC 46 (2003), 181-190.

A. Panayotopoulos and P. Vlamos, Meandric Polygons, Ars Combinatoria 87 (2008), 147-159.

Links

Panayotis Vlamos, Table of n, a(n) for n = 1..22

Iwan Jensen, Enumeration of plane meanders, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.

A. Panayotopoulos and P. Tsikouras, The multimatching property of nested sets, Math. & Sci. Hum. 149 (2000), 23-30.

A. Panayotopoulos and P. Tsikouras, Meanders and Motzkin Words, J. Integer Seqs., Vol. 7, 2004.

A. Panayotopoulos and P. Vlamos, Cutting Degree of Meanders, 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

Prog

(C/C++) int a(int n){
      return w2(i)^2;
}
int w1(int order, int i){
      if (i%2==0) error("error in w1(%d, %d), i is even\n", order, i);
      if (order%2) error("error in w1(%d, %d), order is odd\n", order, i);
      return w2(i+1)*w(order-i+1);
}
int w2(int order){
      if (order%2) error("error in w2(%d), order is odd\n", order);
      return w(order)-w3(order);
}
int w3(int order){
      if (order%2) error("error in w3(%d), order is odd\n", order);
      int sum=0;
      int i;
      for (i=3; i<=order-3; i+=2)
          sum+=w1(order, i);
      return sum;
}
// w(int i), no source here, is the respective meandric number according to Jensen A005315

Crossrefs

Cf. A005315, A192927.

Sequence in context: A095956 A014731 A023114 * A202681 A067211 A156337

Adjacent sequences: A207848 A207849 A207850 * A207852 A207853 A207854

Keyword

nonn

Author

Panayotis Vlamos and Antonios Panayotopoulos, Feb 21 2012

Status

approved