cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A173502 Number of concave kites (darts or arrowheads) on an n X n grid (or geoboard).

Original entry on oeis.org

0, 0, 8, 64, 292, 916, 2344, 5048, 10096, 18296, 31400, 50752, 79308, 118876, 173768, 246096, 342256, 465064, 622904, 818552, 1063756, 1361564, 1725432, 2159384, 2682944, 3298568, 4027776, 4873600
Offset: 1

Views

Author

Martin Renner, Apr 29 2011

Keywords

Examples

			a(1) = 0, since there is only one point on a 1 X 1 grid.
a(2) = 0, since the four points on a 2 X 2 grid build a convex quadrilateral.
a(3) = 8, since there are two possible forms of darts on a 3 X 3 grid, each can appear in four rotations.

Links

Crossrefs

Cf. A189412, A189417.

Extensions

a(7)-a(28) from Nathaniel Johnston, Apr 29 2011

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

Original entry on oeis.org

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

Views

Author

Martin Renner, Apr 03 2012

Keywords

Comments

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

Examples

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

Links

Crossrefs

Cf. A181944, A189417.

Extensions

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

A159944 Number of different deltoids (including squares) whose vertices are on an n X n grid.

Original entry on oeis.org

0, 1, 4, 11, 26, 46, 84, 123, 194, 268, 378, 478, 657, 800, 1019, 1239, 1548, 1793, 2197, 2505, 3003, 3434, 3991, 4444, 5223, 5801, 6582, 7292, 8274, 9006, 10199, 11034, 12330, 13398, 14744, 15912, 17705, 18906, 20586
Offset: 1

Views

Author

Demacek Ondrej (demacek(AT)gjh.sk), Apr 27 2009

Keywords

Comments

Only convex kites (A189417) are counted, not concave kites (A173502), distinct up to congruence.

Examples

			a(1) = 0, since there is only one point on a 1 X 1 grid.
a(2) = 1, since the four points on a 2 X 2 grid build a 1 X 1 square.
a(3) = 4 since there are 3 sizes of squares on a 3 X 3 grid -- 1 X 1, 2 X 2, sqrt(2) X sqrt(2) -- and a single nonsquare deltoid.

Links

Crossrefs

Cf. A189417, A173502.

Extensions

Edited by Ray Chandler, May 01 2011
Corrected and extended by Nathaniel Johnston with help from Ray Chandler, May 11 2011
Showing 1-3 of 3 results.

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