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 A160848 Number of lines through at least 2 points of an 8 X n grid of points. 2
 0, 1, 66, 131, 238, 361, 534, 709, 938, 1183, 1470, 1759, 2104, 2459, 2870, 3287, 3740, 4209, 4734, 5261, 5844, 6437, 7070, 7711, 8408, 9115, 9872, 10637, 11444, 12265, 13142, 14015, 14944, 15889, 16876, 17871, 18914, 19967, 21076, 22193, 23352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 S. Mustonen, On lines and their intersection points in a rectangular grid of points FORMULA a(n) = (1/2)*(f(m,n,1)-f(m,n,2)) where f(m,n,k)=Sum((n-|kx|)*(m-|ky|)); -n21. (End) MATHEMATICA m=8; a[0]=0; a[1]=1; a[2]=m^2+2; a[3]=2*m^2+3-Mod[m, 2]; a[n_]:=a[n]=2*a[n-1]-a[n-2]+2*p1[m, n]+2*p4[m, n] p1[m_, n_]:=Sum[p2[m, n, y], {y, 1, m-1}] p2[m_, n_, y_]:=If[GCD[y, n-1]==1, m-y, 0] p[i_]:=If[i>0, i, 0] p2[m_, n_, x_, y_]:=p2[m, n, x, y]=(n-x)*(m-y)-p[n-2*x]*p[m-2*y] p3[m_, n_, x_, y_]:=p2[m, n, x, y]-2*p2[m, n-1, x, y]+p2[m, n-2, x, y] p4[m_, n_]:=p4[m, n]=If[Mod[n, 2]==0, 0, p42[m, n]] p42[m_, n_]:=p42[m, n]=Sum[p43[m, n, y], {y, 1, m-1}] p43[m_, n_, y_]:=If[GCD[(n-1)/2, y]==1, p3[m, n, (n-1)/2, y], 0] Table[a[n], {n, 0, 40}] CROSSREFS Column k=8 of A295707. Sequence in context: A044189 A044570 A118163 * A160278 A206030 A174929 Adjacent sequences: A160845 A160846 A160847 * A160849 A160850 A160851 KEYWORD nonn AUTHOR Seppo Mustonen, May 28 2009 STATUS approved

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Last modified April 17 02:36 EDT 2024. Contains 371756 sequences. (Running on oeis4.)