

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



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
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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
Math 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



