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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

%I

%S 2,8,18,38,88,115,204,308,375,533,848,693,1405,1377,1627,2116,3121,

%T 2419,4238,4107,4295,5057,7566,5516,9440,8950,9727,10089,14899,10000,

%U 18489,16697,16746,19256,23227,18838,30743,27154,26678,30127,41768,26507,48507,40203,41227

%N 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.

%C First differences of A252591.

%C 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.

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

%e 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.

%Y Cf. A252591.

%K nonn

%O 2,1

%A _Mark S. Fischler_, Dec 27 2014

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