A252592 a(n) = number of new distinct proper angles with vertex and legs on grid points in an n X n square grid that were not found in an (n-1) X (n-1) square grid.

2, 8, 18, 38, 88, 115, 204, 308, 375, 533, 848, 693, 1405, 1377, 1627, 2116, 3121, 2419, 4238, 4107, 4295, 5057, 7566, 5516, 9440, 8950, 9727, 10089, 14899, 10000, 18489, 16697, 16746, 19256, 23227, 18838, 30743, 27154, 26678, 30127, 41768, 26507, 48507, 40203, 41227

Offset

2,1

Comments

First differences of A252591.

The average of the number of distinct angles added by adding six rows and columns to the grid is very nearly a constant times the average grid side cubed. That is, sum_{k=0..5} a(n+k)/6 is close to C*(n+5/2)^3.

a(n)/n^3 is markedly larger for (n-1) prime than for (n-1) composite.

Links

Table of n, a(n) for n=2..46.

Example

a(2) is 2, since no angles can be formed on a single point, while 90- and 45-degree angles can be formed on a 2 X 2 grid. a(3) is 8, since adding those 5 new points to make a 3 X 3 grid allows forming 8 additional angles.

Crossrefs

Cf. A252591.

Sequence in context: A072779 A292764 A198014 * A188577 A064705 A220909

Adjacent sequences: A252589 A252590 A252591 * A252593 A252594 A252595

Keyword

nonn

Author

Mark S. Fischler, Dec 27 2014

Status

approved