login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
3
1, 13, 110, 758, 4617, 25895, 136949, 693369, 3395324, 16197548, 75675657, 347624505, 1574756959, 7051383905, 31266981002, 137492793602, 600295660953, 2604690331787, 11240698270037, 48279130088017, 206486210282936, 879807455701208, 3736101981855305 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

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=6..28.

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: A243417 A163845 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 16 01:36 EST 2017. Contains 296063 sequences.