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 A018808 Number of lines through at least 2 points of an n X n grid of points. 11
 0, 0, 6, 20, 62, 140, 306, 536, 938, 1492, 2306, 3296, 4722, 6460, 8830, 11568, 14946, 18900, 23926, 29544, 36510, 44388, 53586, 63648, 75674, 88948, 104374, 121032, 139966, 160636, 184466, 209944, 239050, 270588, 305478, 342480, 383370, 427020 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 (terms 0..100 from T. D. Noe) A.-M. Ernvall-Hytonen, K. Matomaki, P. Haukkanen, J. K. Merikoski, Formulas for the number of gridlines, Monatsh. f. Mathem. 164 (2) (2011) 157-170 P. Haukkanen, J. K. Merikoski, Some formulas for numbers of line segments and lines in a rectangular grid, arXiv:1108.1041 [math.CO], 2011. FORMULA (1/2) * (f(n, 1) - f(n, 2)) where f(n, k) = Sum ((n - |x|)(n - |y|)); -n < x < n, -n < y < n, (x, y)=k. (1/2) * (f(n, 1) - f(n, 2)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -n < kx < n, -n < ky < n, (x, y)=1. - Seppo Mustonen, Apr 18 2009 a(0) = L(0,1) = R1(0) = 0, a(n) = L(n,n) = 2L(n-1,n) - L(n-1,n-1) + R1(n), L(n-1,n) = 2L(n-1,n-1) - L(n-2,n-1) + R2(n), R1(n) = R1(n-1) + 4(phi(n-1) - e(n)), e(n)=0, n even, e(n) = phi((n-1)/2), n odd, R2(n) = (n-1)phi(n-1), n even, R2(n)=(n-1)phi(n-1)/2, n=1 mod 4, R2(n)=0, n=3 mod 4. - Seppo Mustonen, Apr 25 2009 MATHEMATICA L[0]=0; L1[1]=0; R1[1]=0; L[n_]:=L[n]=2*L1[n]-L[n-1]+R1[n] L1[n_]:=L1[n]=2*L[n-1]-L1[n-1]+R2[n] R1[n_]:=R1[n]=R1[n-1]+4*(EulerPhi[n-1]-e[n]) e[n_]:=If[Mod[n, 2]==0, 0, EulerPhi[(n-1)/2]] R2[n_]:= If[Mod[n, 2]==0, (n-1)*EulerPhi[n-1], If[Mod[n, 4]==1, (n-1)*EulerPhi[n-1]/2, 0]] Table[L[n], {n, 0, 37}] (* Seppo Mustonen, Apr 25 2009 *) CROSSREFS Cf. A222267 (lines defined by n X n X n grid of points). Sequence in context: A109164 A212689 A027984 * A027107 A247307 A279215 Adjacent sequences:  A018805 A018806 A018807 * A018809 A018810 A018811 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)