A371376 - OEIS

%I #8 Mar 22 2024 09:14:26

%S 1,6,3,8,0,1,15,30,5,1,18,30,14,147,35,7,7,1,8,152,48,8,0,0,1,27,351,

%T 171,36,27,10,390,200,10,40,0,0,0,1,22,693,649,33,77,0,0,0,0,1,12,780,

%U 408,0,48,26,1404,1183,234,169,0,0,0,0,0,0,1,14,1498,1274,224,154,14,14,0,0,0,0,0,1

%N Irregular table read by rows: place n equally space points around the circumference of a circle and then, for each pair of points, draw two distinct circles, whose radii are the same as the first circle, such that both points lie on their circumferences. T(n,k), k>=2, gives the number of k-sided regions formed.

%C See A371373 and A371374 for images of the graphs.

%F Sum of row(n) = A371374(n).

%e The table begins:

%e 1;

%e 6, 3;

%e 8, 0, 1;

%e 15, 30, 5, 1;

%e 18, 30;

%e 14, 147, 35, 7, 7, 1;

%e 8, 152, 48, 8, 0, 0, 1;

%e 27, 351, 171, 36, 27;

%e 10, 390, 200, 10, 40, 0, 0, 0, 1;

%e 22, 693, 649, 33, 77, 0, 0, 0, 0, 1;

%e 12, 780, 408, 0, 48;

%e 26, 1404, 1183, 234, 169, 0, 0, 0, 0, 0, 0, 1;

%e 14, 1498, 1274, 224, 154, 14, 14, 0, 0, 0, 0, 0, 1;

%e 45, 2310, 2400, 390, 255, 15;

%e 16, 2736, 2032, 656, 320, 0, 32, 0, 0, 0, 0, 0, 0, 0, 1;

%e 34, 3978, 4097, 969, 493, 17, 34, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 18, 4410, 3078, 972, 468, 36, 18;

%e 76, 6365, 6365, 1596, 855, 95, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 20, 6840, 6000, 2100, 780, 60, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 63, 8946, 10395, 2751, 924, 126, 147;

%e 22, 10076, 9218, 3674, 1166, 22, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 46, 13156, 14996, 4347, 1702, 92, 138, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

%e                                                                      \\ 0, 0, 1;

%e 24, 14232, 13296, 4512, 1440, 96, 240;

%e 100, 19075, 19850, 6975, 2675, 150, 175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

%e                                                                   \\ 0, 0, 0, 1;

%e .

%e .

%Y Cf. A371373 (vertices), A371374 (regions), A371375 (edges), A371377 (vertex crossings), A371274, A331450, A359009, A359061.

%K nonn,tabf

%O 2,2

%A _Scott R. Shannon_, Mar 20 2024