|
| |
|
|
A005770
|
|
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)
|
|
4
| |
|
|
1, 9, 55, 286, 1362, 6143, 26729, 113471, 473471, 1951612, 7974660, 32384127, 130926391, 527657073, 2121795391, 8518575466, 34162154550, 136893468863, 548253828965
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 5,2
|
|
|
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
| 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.
|
|
|
FORMULA
| 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
|
|
|
MAPLE
| 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.]
|
|
|
CROSSREFS
| A005436(n) = A005768(n) + A005769(n) + a(n)
Sequence in context: A068970 A141530 A016269 * A030053 A072844 A026857
Adjacent sequences: A005767 A005768 A005769 * A005771 A005772 A005773
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com), N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Better description from Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
|
| |
|
|
