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A181945 Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard). 2

%I #25 Feb 06 2024 11:33:10

%S 0,1,9,43,141,343,766,1415,2517,4129,6545,9505,14230,19444,26733,

%T 36208,48029,60675,78729,96866,122433,151288,184072,217998,266775,

%U 315096,371138,435153,512549,585240,688470,779196,895058,1019697,1153081,1305629,1494185,1656287

%N Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A181945.py">Python program</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Trapezoid.html">Trapezoid</a>.

%e a(1) = 0 because the 1 X 1 grid has no trapezoids.

%e a(2) = 1 because the 2 X 2 grid has one trapezoid.

%e a(3) = 9 because the 3 X 3 grid has 9 congruence classes of trapezoids, out of 50 trapezoids total:

%e +-------+-------+-------+

%e | . . . | . o . | . . . |

%e | o o . | o . . | o . o |

%e | o o . | o o . | o . o |

%e +-------+-------+-------+

%e | . . o | o . o | . o . |

%e | o . . | . . . | o o . |

%e | o . o | o . o | o . . |

%e +-------+-------+-------+

%e | . o o | . . o | . o . |

%e | o . . | o . o | o . o |

%e | o . . | o . . | . o . |

%e +-------+-------+-------+

%Y Cf. A181944, A189415.

%K nonn

%O 1,3

%A _Martin Renner_, Apr 03 2012

%E a(7)-a(38) from _Lucas A. Brown_, Feb 05 2024

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)