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Search: id:A005770
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| A005770 |
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Number of convex polygons of length 2n on square lattice whose left-most bottom vertex and right-most top vertex have the same x-coordinate.
(Formerly M4638)
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+0
4
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| 1, 9, 55, 286, 1362, 6143, 26729, 113471, 473471, 1951612, 7974660, 32384127, 130926391, 527657073, 2121795391, 8518575466, 34162154550, 136893468863, 548253828965
(list; graph; listen)
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OFFSET
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5,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
M.-P. Delest and G. Viennot, Algebraic languages and polyominoes enumeration, Theoretical Computer Sci., 34 (1984), 169-206.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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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
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MAPLE
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A005770:=(1-3*z+2*z**2+z**3)/(4*z-1)/(2*z-1)/(z**2-3*z+1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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A005436(n) = A005768(n) + A005769(n) + a(n)
Sequence in context: A068970 A141530 A016269 this_sequence A030053 A072844 A026857
Adjacent sequences: A005767 A005768 A005769 this_sequence A005771 A005772 A005773
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com), N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description from Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
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