A373109 - OEIS

%I #7 May 26 2024 08:20:18

%S 8,4,40,76,20,60,492,304,56,20,88,1696,1136,252,64,16,124,4196,3536,

%T 1052,204,28,4,128,8940,7948,2448,496,68,0,4,172,16464,17628,5560,

%U 1268,164,4,144,28424,30884,9964,2064,312,24,8,0,8,196,46844,51840,17832,4112,556,60,20

%N 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 the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

%C A circle is constructed for every pair of the 4 + 4*n points, the two points lying at the ends of a diameter of the circle.

%C See A373106 and A373107 for images of the circles.

%F Sum of row n = A373107(n).

%e The table begins:

%e 8, 4;

%e 40, 76, 20;

%e 60, 492, 304, 56, 20;

%e 88, 1696, 1136, 252, 64, 16;

%e 124, 4196, 3536, 1052, 204, 28, 4;

%e 128, 8940, 7948, 2448, 496, 68, 0, 4;

%e 172, 16464, 17628, 5560, 1268, 164, 4;

%e 144, 28424, 30884, 9964, 2064, 312, 24, 8, 0, 8;

%e 196, 46844, 51840, 17832, 4112, 556, 60, 20;

%e 216, 71944, 80760, 28468, 6272, 856, 136, 0, 4;

%e 264, 106588, 126856, 45148, 10780, 1628, 172, 32, 20;

%e .

%e .

%Y Cf. A373106 (vertices), A373107 (regions), A373108 (edges), A373110 (circles), A372980, A372734, A359009, A362236, A360354.

%K nonn,tabf

%O 0,1

%A _Scott R. Shannon_, May 25 2024