A181947 Number of rhombi, distinct up to congruence, on an n X n grid (or geoboard).

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

Author

Martin Renner, Apr 03 2012

Keywords

• nonn

Examples

			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 . |
+---------+---------+---------+
		

Links

• Lucas A. Brown, Python program.
• Eric Weisstein's World of Mathematics, Rhombus.

Crossrefs

Cf. A181944, A189418.

Extensions

a(7)-a(53) from Lucas A. Brown, Feb 08 2024