A194091 The number of labeled biconnected squaregraphs with perimeter 2*n.

1, 1, 3, 14, 82, 554, 4132, 33154, 281459, 2499523

Offset: 1

Author

Don Knuth, Aug 15 2011

Keywords

• nonn
• hard
• more

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

Examples

			[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).
		

Links

• Don Knuth, squaregraph.w (CWEB program).
• Robert Scherer, Topics in Number Theory and Combinatorics, Ph. D. Dissertation, Univ. of California Davis (2021).

Crossrefs

Cf. A194088, A194089, A194090, A194092, A194093.

Programs

CWEB

(see Knuth link).

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

Extensions

Conjectured terms removed from data by Michael D. Weiner, Aug 03 2017