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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)
3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

REFERENCES

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

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.

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: A026759 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

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Last modified September 22 14:37 EDT 2020. Contains 337291 sequences. (Running on oeis4.)