A001506 a(n) is the number of c-nets with n+1 vertices and 2n edges, n >= 1.

0, 0, 1, 4, 24, 188, 1705, 16980, 180670, 2020120, 23478426, 281481880, 3461873536, 43494961404, 556461656569, 7230987646484, 95244774132810, 1269534571172912, 17100621281619328, 232511930087682528, 3188042426888493288

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..200
• R. C. Mullin and P. J. Schellenberg, The enumeration of c-nets via triangulations, J. Combin. Theory, 4 (1968), 259-276.

Crossrefs

Cf. A290326.

Programs

PARI

A290326(n,k) = {
  if (n < 3 || k < 3, return(0));
  sum(i=0, k-1, sum(j=0, n-1,
     (-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*
     (binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -
      4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));
};
vector(21, n, A290326(n,n))  \\ Gheorghe Coserea, Jul 28 2017

Formula

a(n) = A290326(n,n). - Sean A. Irvine, Sep 29 2015

Extensions

Corrected and extended by Sean A. Irvine, Sep 29 2015

Name changed by Gheorghe Coserea, Jul 23 2017