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A359258
Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.
9
3, 0, 8, 4, 2, 0, 22, 23, 4, 2, 0, 50, 52, 12, 2, 0, 110, 103, 36, 6, 0, 190, 200, 64, 12, 0, 314, 387, 88, 28, 4, 0, 498, 606, 152, 32, 8, 0, 770, 941, 228, 58, 4, 2, 0, 1132, 1352, 338, 68, 12, 2, 0, 1602, 1935, 532, 98, 4, 0, 2122, 2798, 684, 106, 16, 0, 2850, 3843, 940, 132, 24, 6
OFFSET
2,1
COMMENTS
A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
See A359252 and A359253 for other images of the circles.
FORMULA
Sum of row n = A359253(n);
EXAMPLE
The table begins:
3;
0, 8, 4, 2;
0, 22, 23, 4, 2;
0, 50, 52, 12, 2;
0, 110, 103, 36, 6;
0, 190, 200, 64, 12;
0, 314, 387, 88, 28, 4;
0, 498, 606, 152, 32, 8;
0, 770, 941, 228, 58, 4, 2;
0, 1132, 1352, 338, 68, 12, 2;
0, 1602, 1935, 532, 98, 4;
0, 2122, 2798, 684, 106, 16;
0, 2850, 3843, 940, 132, 24, 6;
0, 3774, 4998, 1268, 192, 28, 6;
0, 4950, 6475, 1644, 276, 44, 10;
0, 6190, 8454, 1978, 326, 74, 4;
0, 7778, 10737, 2520, 434, 52, 12, 4;
0, 9674, 13224, 3202, 528, 58, 12, 4;
0, 11978, 16169, 4116, 640, 68, 20, 4;
...
CROSSREFS
Cf. A359253 (regions), A359252 (vertices), A359254 (edges), A001859, A332723, A359061, A359009.
Sequence in context: A317300 A007391 A247668 * A244854 A144807 A157957
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Dec 23 2022
STATUS
approved