A196593 Number of fixed tree-like convex polyominoes.

1, 2, 6, 18, 51, 134, 328, 758, 1677, 3594, 7530, 15530, 31687, 64190, 129420, 260142, 521889, 1045730, 2093806, 4190402, 8384091, 16772022, 33548496, 67102118, 134210101, 268426874, 536861298, 1073731098, 2147471727, 4294954094, 8589920020, 17179853150

Offset

1,2

Comments

In a 1-1 mapping with permutations that avoid the patterns (1423, 4213, 2314, 2431, 2413, <3142,{2},{2}>) (the fourth pattern is bivincular).

Links

Harvey P. Dale, 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

A. Goupil, H. Cloutier, and F. Nouboud, Enumeration of inscribed polyominos, FPSCA 2010 (San Francisco) DMTS proc. AN 2010, 737-748, eq. (10)

Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Formula

G.f.: (x*(1-4*x+8*x^2-6*x^3+4*x^4))/((1-x)^4*(1-2*x)).

a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).

a(n) = 2^(n+2) - (n^3-n^2+10*n+4)/2.

Mathematica

LinearRecurrence[{6, -14, 16, -9, 2}, {1, 2, 6, 18, 51}, 50] (* Harvey P. Dale, Oct 16 2011 *)

Crossrefs

Cf. A001168 (fixed polyominoes), A066158 (fixed tree polyominoes), A067675 (fixed convex polyominoes).

Sequence in context: A309087 A199770 A204322 * A248735 A219136 A192237

Adjacent sequences: A196590 A196591 A196592 * A196594 A196595 A196596

Keyword

nonn,easy

Author

Gill Barequet, Oct 04 2011

Status

approved