A386560
Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite regions created in the resulting graph.
Original entry on oeis.org
4, 72, 424, 1396, 3536, 7292, 14272, 24332, 39356, 59920, 91348, 128084, 182664, 245804, 323116, 418552, 547820, 684680, 869388, 1060892, 1289564, 1560920
Offset: 1
A386562
Irregular table read by rows: Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: T(n,k) is the number of k-sided finite polygons formed, for k>=3, in the resulting graph.
Original entry on oeis.org
4, 44, 24, 4, 184, 216, 24, 560, 780, 56, 1456, 1844, 224, 12, 3100, 3788, 376, 24, 4, 5860, 7100, 1148, 156, 8, 9860, 12436, 1848, 164, 20, 4, 16044, 19732, 3100, 460, 16, 4, 24744, 29568, 5048, 516, 32, 12, 36780, 43472, 9608, 1400, 68, 20, 52296, 61244, 12628, 1784, 116, 16
Offset: 1
The table begins:
4;
44, 24, 4;
184, 216, 24;
560, 780, 56;
1456, 1844, 224, 12;
3100, 3788, 376, 24, 4;
5860, 7100, 1148, 156, 8;
9860, 12436, 1848, 164, 20, 4;
16044, 19732, 3100, 460, 16, 4;
24744, 29568, 5048, 516, 32, 12;
36780, 43472, 9608, 1400, 68, 20;
52296, 61244, 12628, 1784, 116, 16;
72492, 85672, 20424, 3792, 268, 16;
97812, 115000, 27796, 4820, 344, 24, 8;
129416, 151184, 35716, 6240, 532, 28;
167712, 195816, 46380, 7956, 644, 44;
.
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- Scott R. Shannon, Image for n = 2. The integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.
A386561
Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite edges created in the resulting graph.
Original entry on oeis.org
8, 136, 804, 2608, 6568, 13396, 26556, 45120, 73060, 110984, 171144, 238900, 344212, 462788, 607384, 786476, 1037772, 1293904, 1654432, 2013768, 2447312, 2965392
Offset: 1
A386775
Place a point on the integer coordinates, up to |k|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the smallest k such that n lines intersect at a point not on the axes.
Original entry on oeis.org
2, 3, 4, 6, 8, 9, 9, 10, 14, 16, 18, 20, 24, 25, 26, 30, 34, 36
Offset: 2
a(9) = 10 as the following 9 lines all intersect at the point (4,3) while having |x| and |y| intercepts <= 10 :
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equation | y-intercept | x-intercept
-------------------------------------------------
-3/2*x + 9 | 9 | 6
-x + 7 | 7 | 7
-3/4*x + 6 | 6 | 8
-1/2*x + 5 | 5 | 10
1/4*x + 2 | 2 | -8
1/2*x + 1 | 1 | -2
x - 1 | -1 | 1
3/2*x - 3 | -3 | 2
3*x - 9 | -9 | 3
-------------------------------------------------
Showing 1-4 of 4 results.
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