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A005770 Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex and rightmost top vertex have the same x-coordinate.
(Formerly M4638)
4

%I M4638

%S 1,9,55,286,1362,6143,26729,113471,473471,1951612,7974660,32384127,

%T 130926391,527657073,2121795391,8518575466,34162154550,136893468863,

%U 548253828965,2194897467395,8784784672511,35153438973304,140653028240520,562719731644671

%N Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex and rightmost top vertex have the same x-coordinate.

%D M.-P. Delest and G. Viennot, Algebraic languages and polyominoes enumeration, Theoretical Computer Sci., 34 (1984), 169-206.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%F a(n) = A005436(n) - A005768(n) - A005769(n).

%F G.f.: x^5*(1-3*x+2*x^2+x^3)/((1-2*x^(1/2))*(1+2*x^(1/2))*(1-2*x)*(1+x^(1/2)-x)^2*(1-x^(1/2)-x)^2). - Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003

%p A005770:=(1-3*z+2*z**2+z**3)/(4*z-1)/(2*z-1)/(z**2-3*z+1)**2; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%K nonn,easy

%O 5,2

%A _Simon Plouffe_, _N. J. A. Sloane_

%E Better description from Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003

%E More terms from _Sean A. Irvine_, Aug 26 2016

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Last modified October 1 11:59 EDT 2020. Contains 337443 sequences. (Running on oeis4.)