A001506 a(n) is the number of c-nets with n+1 vertices and 2n edges, n >= 1. (Formerly M3603 N1462)

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

Offset

1,4

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.

Formula

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

Prog

(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

Crossrefs

Cf. A290326.

Sequence in context: A239296 A028498 A001397 * A354123 A088815 A366367

Adjacent sequences: A001503 A001504 A001505 * A001507 A001508 A001509

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Name changed by Gheorghe Coserea, Jul 23 2017

Status

approved