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%I #29 Jul 17 2022 10:29:40
%S 1,2,6,18,51,134,328,758,1677,3594,7530,15530,31687,64190,129420,
%T 260142,521889,1045730,2093806,4190402,8384091,16772022,33548496,
%U 67102118,134210101,268426874,536861298,1073731098,2147471727,4294954094,8589920020,17179853150
%N Number of fixed tree-like convex polyominoes.
%C In a 1-1 mapping with permutations that avoid the patterns (1423, 4213, 2314, 2431, 2413, <3142,{2},{2}>) (the fourth pattern is bivincular).
%H Harvey P. Dale, <a href="/A196593/b196593.txt">Table of n, a(n) for n = 1..1000</a>
%H Gadi Aleksandrowicz, Andrei Asinowski and Gill Barequet, <a href="http://dx.doi.org/10.1016/j.jcta.2011.10.008">A polyominoes-permutations injection and tree-like convex polyominoes</a>, Journal of Combinatorial Theory, Series A, Volume 119, Issue 3, April 2012, Pages 503-520
%H A. Goupil, H. Cloutier, and F. Nouboud, <a href="https://hal.inria.fr/hal-01186234">Enumeration of inscribed polyominos</a>, FPSCA 2010 (San Francisco) DMTS proc. AN 2010, 737-748, eq. (10)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F G.f.: (x*(1-4*x+8*x^2-6*x^3+4*x^4))/((1-x)^4*(1-2*x)).
%F a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).
%F a(n) = 2^(n+2) - (n^3-n^2+10*n+4)/2.
%t LinearRecurrence[{6,-14,16,-9,2},{1,2,6,18,51},50] (* _Harvey P. Dale_, Oct 16 2011 *)
%Y Cf. A001168 (fixed polyominoes), A066158 (fixed tree polyominoes), A067675 (fixed convex polyominoes).
%K nonn,easy
%O 1,2
%A _Gill Barequet_, Oct 04 2011