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A181947
Number of rhombi, distinct up to congruence, on an n X n grid (or geoboard).
2
0, 1, 3, 6, 11, 16, 24, 31, 43, 53, 67, 78, 99, 112, 132, 151, 179, 196, 226, 245, 282, 309, 341, 364, 416, 445, 483, 517, 570, 599, 659, 690, 754, 797, 847, 894, 975, 1012, 1068, 1119, 1211, 1252, 1338, 1381, 1466, 1536, 1604, 1651, 1775, 1833, 1923, 1990, 2091
OFFSET
1,3
LINKS
Lucas A. Brown, Python program.
Eric Weisstein's World of Mathematics, Rhombus.
EXAMPLE
a(1) = 0 because the 1 X 1 grid has no rhombi.
a(2) = 1 because the 2 X 2 grid has one rhombus.
a(3) = 3 because the 3 X 3 grid has 3 congruence classes of rhombi (all of which are squares) out of 6 rhombi total.
a(3) = 6 because the 4 X 4 grid has 6 congruence classes of rhombi, out of 22 rhombi 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 . |
+---------+---------+---------+
CROSSREFS
Sequence in context: A116940 A278100 A087099 * A366969 A075703 A267583
KEYWORD
nonn
AUTHOR
Martin Renner, Apr 03 2012
EXTENSIONS
a(7)-a(53) from Lucas A. Brown, Feb 08 2024
STATUS
approved