A067675 Number of fixed convex polyominoes with n cells.

1, 2, 6, 19, 59, 176, 502, 1374, 3630, 9312, 23320, 57279, 138536, 331032, 783630, 1841867, 4306172, 10028276, 23288394, 53974959, 124925967, 288878550, 667602492, 1542254655, 3562000916, 8225719574, 18994263354, 43858728367, 101270779744, 233836327750, 539935689810

Offset: 1

Author

Steven Finch, Feb 04 2002

Keywords

• nonn

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.19, p. 380.

Links

• Ruben Grønning Spaans, Table of n, a(n) for n = 1..1000
• Gadi Aleksandrowicz, Andrei Asinowski and Gill Barequet, A polyominoes-permutations injection and tree-like convex polyominoes, Journal of Combinatorial Theory, Series A, Volume 119, Issue 3, April 2012, Pages 503-520.
• M. Bousquet-Mélou and J.-M. Fédou, The generating function of convex polyominoes: the resolution of a q-differential system, Discrete Math. 137 (1995) 53-75.
• Ruben Grønning Spaans, C program.
• V. M. Zhuravlev, Horizontally-convex polyiamonds and their generating functions, Mat. Pros. 17 (2013), 107-129 (in Russian).

Crossrefs

Cf. A006958, A067676 (fixed directed convex polyominoes), A191148 (fixed line-convex polycubes in 3 dimensions), A276994.

Formula

a(n) ~ c * d^n, where d = A276994 = 2.309138593330494731098720305017212531911814472581628401694402900284456440748..., c = 2.91959850971360705538470951565133568591516894147305658630679268977185945... . - Vaclav Kotesovec, Sep 27 2016

Extensions

Six more terms from Ruben Grønning Spaans, Sep 20 2014