

A177726


Number of line segments connecting exactly 10 points in an n x n grid of points


0



0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 52, 90, 136, 190, 252, 322, 400, 486, 620, 770, 936, 1118, 1316, 1530, 1760, 2006, 2268, 2662, 3088, 3546, 4036, 4558, 5112, 5698, 6316, 6966, 7800, 8682, 9612, 10590, 11616, 12690, 13812, 14982, 16200, 17842, 19564, 21366
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,10


COMMENTS

a(n) is also the number of pairs of points visible to each other exactly through 8 points in an n x n grid of points.


LINKS

Table of n, a(n) for n=1..48.
S. Mustonen, On lines going through a given number of points in a rectangular grid of points


FORMULA

See Mathematica code.


MATHEMATICA

j=9;
a[n_]:=a[n]=If[n<=j, 0, 2*a1[n]a[n1]+R1[n]]
a1[n_]:=a1[n]=If[n<=j, 0, 2*a[n1]a1[n1]+R2[n]]
R1[n_]:=R1[n]=If[n<=j, 0, R1[n1]+4*S[n]]
R2[n_]:=(n1)*S[n]
S[n_]:=If[Mod[n1, j]==0, EulerPhi[(n1)/j], 0]
Table[a[n], {n, 1, 50}]


CROSSREFS

Sequence in context: A200880 A111576 A277979 * A101571 A290381 A324486
Adjacent sequences: A177723 A177724 A177725 * A177727 A177728 A177729


KEYWORD

nonn


AUTHOR

Seppo Mustonen, May 13 2010


STATUS

approved



