

A194091


The number of labeled biconnected squaregraphs with perimeter 2*n.


5




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 3noncrossing perfect matchings on [2n] (compare to A005700).  Michael D. Weiner, Jun 09 2017


LINKS

Table of n, a(n) for n=1..10.
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



