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

1,3

Links

Table of n, a(n) for n=1..53.

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

Cf. A181944, A189418.

Sequence in context: A116940 A278100 A087099 * A366969 A075703 A267583

Adjacent sequences: A181944 A181945 A181946 * A181948 A181949 A181950

Keyword

nonn

Author

Martin Renner, Apr 03 2012

Extensions

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

Status

approved