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

1,2

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).

Formula

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

Crossrefs

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

Sequence in context: A307564 A308240 A328658 * A037512 A111277 A014346

Adjacent sequences: A067672 A067673 A067674 * A067676 A067677 A067678

Keyword

nonn

Author

Steven Finch, Feb 04 2002

Extensions

Six more terms from Ruben Grønning Spaans, Sep 20 2014

Status

approved