A252591 Number of distinct proper angles that can be formed by a vertex and two leg endpoints on grid points in an n X n square grid.

2, 10, 28, 66, 154, 269, 473, 781, 1156, 1689, 2537, 3230, 4635, 6012, 7639, 9755, 12876, 15295, 19533, 23640, 27935, 32992, 40558, 46074, 55514, 64464, 74191, 84280, 99179, 109179, 127668, 144365, 161111, 180367, 203594, 222432, 253175, 280329, 307007, 337134, 378902, 405409, 453916, 494119, 535346

Offset

2,1

Comments

a(n)/n^4 lies in the interval[0.112, 0.123] for all 5 < n < 120.

Links

Mark S. Fischler, Table of n, a(n) for n = 2..115

Mark S. Fischler, CPP code which generates up to 118 terms

Mathematics Stack Exchange user Adhvaitha, Number of distinct angles that can be formed on a square grid

Example

For n=2, a(2)=2 as only angles of Pi/2 and Pi/4 can be formed on the vertices of a 2 X 2 square. For n=3, 8 additional angles can be formed, including 3*Pi/4 and one other obtuse angle, and six new acute angles; thus a(3)=10.

Prog

(C++) See links.

Crossrefs

Sequence in context: A109723 A053594 A006331 * A296849 A296380 A291053

Adjacent sequences: A252588 A252589 A252590 * A252592 A252593 A252594

Keyword

nonn

Author

Mark S. Fischler, Dec 18 2014

Status

approved