A187014 Number of isomorphism classes of simply embedded (i.e., loop-free and without parallel edges bounding a disk) bipartite quadrangulations of RP^2 of minimum degree 3 with n nodes and n-1 faces.

0, 0, 1, 2, 3, 7, 22, 57, 174, 554, 1848, 6291, 22052, 78361, 282420, 1027336

Offset

4,4

Comments

Also the number of isomorphism classes of homologically trivial basic nets on RP^2 with n-1 nodes and n faces.

Also the number of isomorphism classes of simple quadrangulations of the sphere of minimum degree 3 with 2n nodes and 2n-2 faces which admit an orientation reversing involution without fix nodes and fix edges such that the bipartite coloring is preserved under the involution.

Links

Table of n, a(n) for n=4..19.

S. Yu. Orevkov, Basic nets in the projective plane, Ann. Fac. Sci. Toulouse Math., 24 (2015), 205-226; arXiv:1307.7377 [math.CO], 2013-2014.

Crossrefs

Cf. A078666, A187013.

Sequence in context: A155745 A067738 A296287 * A053966 A010738 A114599

Adjacent sequences: A187011 A187012 A187013 * A187015 A187016 A187017

Keyword

nonn,more,changed

Author

Stepan Orevkov, Aug 30 2013

Extensions

a(19) from Orevkov added by Andrei Zabolotskii, May 31 2026

Status

approved