Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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