A181945 - OEIS

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A181945

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

0, 1, 9, 43, 141, 343, 766, 1415, 2517, 4129, 6545, 9505, 14230, 19444, 26733, 36208, 48029, 60675, 78729, 96866, 122433, 151288, 184072, 217998, 266775, 315096, 371138, 435153, 512549, 585240, 688470, 779196, 895058, 1019697, 1153081, 1305629, 1494185, 1656287

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..38.

Lucas A. Brown, Python program.

Eric Weisstein's World of Mathematics, Trapezoid.

EXAMPLE

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

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

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

+-------+-------+-------+

| . . . | . o . | . . . |

| o o . | o . . | o . o |

| o o . | o o . | o . o |

+-------+-------+-------+

| . . o | o . o | . o . |

| o . . | . . . | o o . |

| o . o | o . o | o . . |

+-------+-------+-------+

| . o o | . . o | . o . |

| o . . | o . o | o . o |

| o . . | o . . | . o . |

+-------+-------+-------+

CROSSREFS

Cf. A181944, A189415.

Sequence in context: A185918 A116015 A332373 * A244869 A259181 A330088

Adjacent sequences: A181942 A181943 A181944 * A181946 A181947 A181948

KEYWORD

nonn

AUTHOR

Martin Renner, Apr 03 2012

EXTENSIONS

a(7)-a(38) from Lucas A. Brown, Feb 05 2024

STATUS

approved