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A371377 Irregular table read by rows: place n equally spaced 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 vertices formed by the crossing of k arcs.

%I A371377 #12 Jun 02 2025 22:29:37
%S A371377 0,0,0,4,0,4,10,10,0,5,6,6,0,6,1,98,35,0,0,0,7,104,32,0,0,0,8,369,81,
%T A371377 0,0,0,0,0,10,410,80,0,0,0,0,0,10,1034,165,0,0,0,0,0,0,0,11,768,84,0,
%U A371377 0,36,0,0,0,0,12,1,2288,286,0,0,0,0,0,0,0,0,0,13,2464,280,0,0,0,0,0,0,0,0,0,14
%N A371377 Irregular table read by rows: place n equally spaced 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 vertices formed by the crossing of k arcs.
%C A371377 See A371373 and A371374 for images of the graphs.
%F A371377 Sum of row(n) = A371373(n).
%e A371377 The table begins:
%e A371377 0;
%e A371377 0;
%e A371377 0, 4;
%e A371377 0, 4;
%e A371377 10, 10, 0, 5;
%e A371377 6, 6, 0, 6, 1;
%e A371377 98, 35, 0, 0, 0, 7;
%e A371377 104, 32, 0, 0, 0, 8;
%e A371377 369, 81, 0, 0, 0, 0, 0, 10;
%e A371377 410, 80, 0, 0, 0, 0, 0, 10;
%e A371377 1034, 165, 0, 0, 0, 0, 0, 0, 0, 11;
%e A371377 768, 84, 0, 0, 36, 0, 0, 0, 0, 12, 1;
%e A371377 2288, 286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13;
%e A371377 2464, 280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14;
%e A371377 4230, 420, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16;
%e A371377 4672, 448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16;
%e A371377 7990, 680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17;
%e A371377 7254, 450, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 1;
%e A371377 13148, 969, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19;
%e A371377 13620, 960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20;
%e A371377 20265, 1323, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22;
%e A371377 21230, 1320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22;
%e A371377 30452, 1771, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23;
%e A371377 29376, 1416, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1;
%e A371377 43800, 2300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25;
%e A371377 45136, 2288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26;
%e A371377 .
%e A371377 .
%Y A371377 Cf. A371373 (vertices), A371374 (regions), A371375 (edges), A371376 (k-gons), A371264, A335102, A007569, A358746, A331702.
%K A371377 nonn,tabf
%O A371377 1,4
%A A371377 _Scott R. Shannon_, Mar 20 2024