A181946 Number of kites, distinct up to congruence, on an n X n grid (or geoboard).

0, 1, 4, 11, 25, 45, 81, 121, 188, 261, 368, 469, 641, 785, 1000, 1220, 1520, 1767, 2161, 2471, 2961, 3396, 3946, 4403, 5164, 5744, 6517, 7227, 8201, 8936, 10122, 10963, 12240, 13312, 14649, 15839, 17607, 18813, 20482, 21983, 24111, 25589, 27920, 29550, 31979

Offset

1,3

Comments

Only convex kites are counted, not concave kites (sometimes called darts or arrowheads).

Links

Table of n, a(n) for n=1..45.

Lucas A. Brown, Python program.

Eric Weisstein's World of Mathematics, Kite.

Example

a(1) = 0 because the 1 X 1 grid has no kites.
a(2) = 1 because the 2 X 2 grid has one kite.
a(3) = 4 because the 3 X 3 grid has 4 congruence classes of kites, out of 10 kites total:
+-------+-------+-------+-------+
| . . . | o . o | . . o | . o . |
| o o . | . . . | o . . | o . o |
| o o . | o . o | o o . | . o . |
+-------+-------+-------+-------+

Crossrefs

Cf. A181944, A189417.

Sequence in context: A349569 A349570 A192597 * A176959 A115294 A110610

Adjacent sequences: A181943 A181944 A181945 * A181947 A181948 A181949

Keyword

nonn

Author

Martin Renner, Apr 03 2012

Extensions

a(7)-a(45) from Lucas A. Brown, Feb 08 2024

Status

approved