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A181945
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Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).
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2
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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;
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listen;
history;
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OFFSET
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1,3
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LINKS
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Eric Weisstein's World of Mathematics, Trapezoid.
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EXAMPLE
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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 . |
+-------+-------+-------+
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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