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A225606 Number of distinct lines passing through 3 or more points in an n X n grid. 4
0, 0, 0, 8, 14, 32, 58, 108, 174, 296, 406, 628, 898, 1216, 1582, 2188, 2754, 3528, 4398, 5524, 6778, 8336, 9778, 11812, 14038, 16456, 19066, 22540, 25954, 29968, 34270, 39116, 44282, 50312, 56026, 63196, 70798, 78984 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..37.

P. Haukkanen, J. K. Merikoski, Some formulas for numbers of line segments and lines in a rectangular grid, arXiv:1108.1041

R. J. Mathar, Maple program implementing A225606, A018808 and sequ. in comment of A187397

FORMULA

a(n) = A018808(n) - A018809(n) = A018810(n) + A018811(n) + A018812(n) + A018813(n)+....

MATHEMATICA

f[n_, k_] := Sum[x = kx/k; y = ky/k; If[IntegerQ[x] && IntegerQ[y] && CoprimeQ[x, y], (n - Abs[kx])(n - Abs[ky]), 0], {kx, -n + 1, n - 1}, {ky, -n + 1, n - 1}];

a[n_] := (f[n, 2] - f[n, 3])/2;

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Oct 30 2018, after Seppo Mustonen in A018808 *)

CROSSREFS

Sequence in context: A273843 A227867 A254034 * A117132 A064969 A236332

Adjacent sequences:  A225603 A225604 A225605 * A225607 A225608 A225609

KEYWORD

nonn

AUTHOR

R. J. Mathar, Aug 06 2013

STATUS

approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)