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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)