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URL: https://oeis.org/A005769

⇱ A005769 - OEIS

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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.
3
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
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
KEYWORD
nonn,easy
AUTHOR
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