%I M4911 #26 Jan 08 2024 04:34:48

%S 1,13,110,758,4617,25895,136949,693369,3395324,16197548,75675657,

%T 347624505,1574756959,7051383905,31266981002,137492793602,

%U 600295660953,2604690331787,11240698270037,48279130088017,206486210282936,879807455701208,3736101981855305

%N Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the right 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) - A005768(n) - A005770(n).

%F G.f.: x^4 * (2 - 20*x + 75*x^2 - 127*x^3 + 95*x^4 - 27*x^5 + 4*x^6) / ((1 - 2*x^(1/2))^2 * (1 + 2*x^(1/2))^2 * (1 - 2*x) * (1 + x^(1/2) - x)^2 * (1 - x^(1/2) - x)^2) - 2*x^4 * (1 - 4*x)^(-3/2). - Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003

%t DeleteCases[CoefficientList[Series[x^4*(2 - 20 x + 75 x^2 - 127 x^3 + 95 x^4 - 27 x^5 + 4 x^6)/((1 - 2 x^(1/2))^2*(1 + 2 x^(1/2))^2*(1 - 2 x) (1 + x^(1/2) - x)^2*(1 - x^(1/2) - x)^2) - 2 x^4*(1 - 4 x)^(-3/2), {x, 0, 27}], x] , 0] (* _Michael De Vlieger_, Aug 26 2016 *)

%K nonn,easy

%O 6,2

%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