A001508 a(n) is the number of c-nets with n+1 vertices and 2n+2 edges, n >= 1. (Formerly M4918 N2111)

0, 0, 0, 0, 13, 252, 3740, 51300, 685419, 9095856, 120872850, 1614234960, 21697730835, 293695935764, 4003423965684, 54944523689692, 758990230992175, 10548884795729280, 147458773053913268, 2072369440050644208, 29271357456284966994

Offset

1,5

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..204

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+2,n). - Gheorghe Coserea, Jul 28 2017

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+2, n)) \\ Gheorghe Coserea, Jul 28 2017

Crossrefs

Cf. A290326.

Sequence in context: A286878 A106738 A332849 * A157946 A352653 A321849

Adjacent sequences: A001505 A001506 A001507 * A001509 A001510 A001511

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