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. (Formerly M4911)

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

Offset

6,2

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=6..28.

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

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

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 *)

Crossrefs

Sequence in context: A163845 A380001 A075143 * A042941 A021344 A119744

Adjacent sequences: A005766 A005767 A005768 * A005770 A005771 A005772

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