A005769 Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the right of the rightmost top vertex.

1, 13, 110, 758, 4617, 25895, 136949, 693369, 3395324, 16197548, 75675657, 347624505, 1574756959, 7051383905, 31266981002, 137492793602, 600295660953, 2604690331787, 11240698270037, 48279130088017, 206486210282936, 879807455701208, 3736101981855305

Offset: 6

Author

Simon Plouffe

Keywords

• nonn
• easy

References

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

Links

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

Programs

Mathematica

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 *)

Formula

a(n) = A005436(n) - A005768(n) - A005770(n).

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

Extensions

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

More terms from Sean A. Irvine, Aug 26 2016