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A196593
Number of fixed tree-like convex polyominoes.
1
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
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)
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
KEYWORD
nonn,easy
AUTHOR
Gill Barequet, Oct 04 2011
STATUS
approved