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%I M1776 #24 Jan 08 2024 02:20:35
%S 1,2,7,27,110,460,1948,8296,35400,151056,643892,2740216,11639416,
%T 49340080,208727176,881212272,3713043152,15615663008,65555425780,
%U 274734294328,1149506252376,4802212126704,20032666552664,83452195924304,347192769717040,1442672957396320
%N Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the left of the rightmost top vertex.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M.-P. Delest and G. Viennot, <a href="https://doi.org/10.1016/0304-3975(84)90116-6">Algebraic languages and polyominoes enumeration</a>, Theoretical Computer Sci., 34 (1984), 169-206.
%F a(n) = A005436(n) - A005769(n) - A005770(n).
%F G.f.: x^2 * (1 - 8*x + 21*x^2 - 19*x^3 + 4*x^4) / ((1 - 2*x^(1/2))^2 * (1 + 2*x^(1/2))^2*(1 - 2*x)) - 2*x^4*(1 - 4*x)^(-3/2). - Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
%t DeleteCases[CoefficientList[Series[x^2*(1 - 8 x + 21 x^2 - 19 x^3 + 4 x^4)/((1 - 2 x^(1/2))^2*(1 + 2 x^(1/2))^2*(1 - 2 x)) - 2 x^4*(1 - 4 x)^(-3/2), {x, 0, 25}], x] , 0] (* _Michael De Vlieger_, Aug 26 2016 *)
%K nonn,easy
%O 2,2
%A _Simon Plouffe_
%E Better description from Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
%E More terms from _Sean A. Irvine_, Aug 26 2016