A005768 Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the left of the rightmost top vertex. (Formerly M1776)

1, 2, 7, 27, 110, 460, 1948, 8296, 35400, 151056, 643892, 2740216, 11639416, 49340080, 208727176, 881212272, 3713043152, 15615663008, 65555425780, 274734294328, 1149506252376, 4802212126704, 20032666552664, 83452195924304, 347192769717040, 1442672957396320

Offset

2,2

References

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

Links

Table of n, a(n) for n=2..27.

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

Formula

a(n) = A005436(n) - A005769(n) - A005770(n).

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

Mathematica

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 *)

Crossrefs

Sequence in context: A361778 A150599 A150600 * A150601 A150602 A150603

Adjacent sequences: A005765 A005766 A005767 * A005769 A005770 A005771

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

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

More terms from Sean A. Irvine, Aug 26 2016

Status

approved