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)

1, 9, 55, 286, 1362, 6143, 26729, 113471, 473471, 1951612, 7974660, 32384127, 130926391, 527657073, 2121795391, 8518575466, 34162154550, 136893468863, 548253828965, 2194897467395, 8784784672511, 35153438973304, 140653028240520, 562719731644671

Offset

5,2

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=5..28.

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

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Formula

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

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

Maple

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

Crossrefs

Sequence in context: A263478 A326249 A016269 * A030053 A072844 A026857

Adjacent sequences: A005767 A005768 A005769 * A005771 A005772 A005773

Keyword

nonn,easy

Author

Simon Plouffe, N. J. A. Sloane

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