The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194091 The number of labeled biconnected squaregraphs with perimeter 2*n. 5
 1, 1, 3, 14, 82, 554, 4132, 33154, 281459, 2499523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: The next terms are 23031395, 218862682, 2134993642, 21301755122, 216752986922, 2243977451994, 23590001630055, 251411579942151. - Michael D. Weiner, Apr 07 2016 Conjecture: a(n) is also the number of connected 3-noncrossing perfect matchings on [2n] (compare to A005700). - Michael D. Weiner, Jun 09 2017 LINKS Don Knuth, squaregraph.w (CWEB program). Robert Scherer, Topics in Number Theory and Combinatorics, Ph. D. Dissertation, Univ. of California Davis (2021). FORMULA G.f.: A(x) satisfies A(x*T(x)^2) = T(x)-1 where T(x) is the o.g.f. for A005700 (conjectured). - Michael D. Weiner, Jun 09 2017 EXAMPLE [See A194090 for the definition of "labeled squaregraph".] For n=4 the a(4)=14 labeled biconnected squaregraphs of perimeter 8 are the straight tromino (with 4 labelings), the L tromino (with 8), and the square tetromino (with 2). PROG (CWEB) (see Knuth link). CROSSREFS Cf. A194088, A194089, A194090, A194092, A194093. Sequence in context: A032080 A291535 A333956 * A186737 A020104 A220894 Adjacent sequences:  A194088 A194089 A194090 * A194092 A194093 A194094 KEYWORD nonn,hard,more AUTHOR Don Knuth, Aug 15 2011 EXTENSIONS Conjectured terms removed from data by Michael D. Weiner, Aug 03 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 28 05:59 EDT 2021. Contains 346317 sequences. (Running on oeis4.)