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A181945
Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).
3
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
OFFSET
1,3
LINKS
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
Sequence in context: A185918 A116015 A332373 * A244869 A259181 A330088
KEYWORD
nonn
AUTHOR
Martin Renner, Apr 03 2012
EXTENSIONS
a(7)-a(38) from Lucas A. Brown, Feb 05 2024
STATUS
approved