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A273089 Number of lattice n-gons with ordered sides 1, 2, 3, ..., n. 1
0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 5, 6, 0, 0, 584, 882, 0, 0, 18026, 194741, 0, 0, 644414, 960834, 0, 0, 229910636 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

First 16 terms calculated by Stefan Kohl.

LINKS

Table of n, a(n) for n=1..27.

Stefan Kohl, Lattice n-gons with ordered side lengths 1,2,3,…,n, Answer on MathOverflow, May 4, 2016.

MathOverflow, Lattice n-gons with ordered side lengths 1,2,3,...,n

Giovanni Resta, Examples of n-gons with minimal and maximal area

L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324.

Wikipedia, Golygon

EXAMPLE

a(8) = 3:

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  ._._._._._| . | .   | . . .   . . |    | . . . . . . |

  | . . . . . . | .   | . . . |\. . |    | . . . . . . |

  | . . . . . . | .   | . . . | \ . |    | ._._._. . . |

  | . . . . . . | .   | . . . | .\5 |    | | . . | . ./.

  | . . . . . . | .   | ._._._| . .\|    |_| . . | ./5 .

  | . . . . . . | .   | | . . . . . .    . . . . | / . .

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.

a(11) = 5:

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  . . . . . . . | . . | . . . . .10 . . . | . . . . . . .

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  |\. . . . . | . . . . . 5 \ . . . . . | . . . . . . . |

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  | . . 10. . | . | . . . . . . . . . . | . . . | . 5 . |

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  | . . . . \ | . | . . . . . . . . . . | ._._._| . . . .

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  | . . . .\. . . . . . . . . . . . . . .10 . . | . . . . . . . .

  | . . . . . 5 . . . . . . . . . . . . / . . . | . . . . . . . .

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  | . . . . . . . | . . . . . . . . | . . . . . |_._._._._._._._.

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  | . . . . . . . |_._._._._._._. . | . . . . . . . . . . . . . |

  .\. . . . . . . . . . . . . . | . | . . . | \ . . . . . . . . |

  . \ . . . . . . . . . . . . . | . | . . . | . .5. . . . . . . |

  . . \ . . . . . . . . . . . . | . | . . . | . . .\._._._._._._|

  . . . \ . . . . . . . . . . . | . | ._._._| . . . . . . . . . .

  . . . 10. . . . . . . . . . . | . | | . . . . . . . . . . . . .

  . . . . \ . . . . . . . . . . | . |_| . . . . . . . . . . . . .

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  |_| . . | . . ./| . . . . . . |

  . . . . | . 5 . | . . . . . . |

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  . . . . . . . . |_._._._._._._|

. - Hugo Pfoertner, Mar 20 2020

CROSSREFS

Cf. A007219.

Sequence in context: A316511 A317465 A051174 * A330735 A127773 A194498

Adjacent sequences:  A273086 A273087 A273088 * A273090 A273091 A273092

KEYWORD

nonn,hard,more

AUTHOR

Bernardo Recamán, May 14 2016

EXTENSIONS

Typo in a(15) corrected and a(17)-a(27) added by Giovanni Resta, Mar 26 2020

STATUS

approved

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Last modified January 27 13:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)