A006725 Number of n-celled polygons with perimeter 2n+2 on square lattice. (Formerly M1623)

1, 2, 6, 18, 55, 174, 566, 1868, 6237, 21050, 71666, 245696, 847317, 2937116, 10226574, 35746292, 125380257, 441125966, 1556301578, 5504340656, 19511769838, 69307575896, 246650185778, 879290186630, 3139599571529, 11226785625786, 40200300651608, 144129982276422

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Andrei Zabolotskii, Table of n, a(n) for n = 1..50

I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484.

Michael E. Fisher, Anthony J. Guttmann and Stuart G. Whittington, Two-dimensional lattice vesicles and polygons, J. Phys. A: Math. Gen., 24 (1991), 3095-3106; alternative link.

Iwan Jensen, Series Expansions for Self-Avoiding Polygons. See Number of SAP of given area and any perimeter.

Crossrefs

Cf. A008855.

Sequence in context: A238236 A294159 A000778 * A066158 A148456 A148457

Adjacent sequences: A006722 A006723 A006724 * A006726 A006727 A006728

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Title corrected by David Bevan, Sep 28 2011

a(20) corrected (was 18155586993) and terms a(21) onward from Jensen added by Andrei Zabolotskii, Sep 11 2025

Status

approved