cp's OEIS Frontend

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.

%I A386562 #8 Aug 02 2025 10:00:34
%S A386562 4,44,24,4,184,216,24,560,780,56,1456,1844,224,12,3100,3788,376,24,4,
%T A386562 5860,7100,1148,156,8,9860,12436,1848,164,20,4,16044,19732,3100,460,
%U A386562 16,4,24744,29568,5048,516,32,12,36780,43472,9608,1400,68,20,52296,61244,12628,1784,116,16
%N 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.
%C A386562 For graphs up to n = 22 the k-gons with the largest number of sides are 12-gons, first appearing for n = 20. The behavior of this maximum value as n -> infinity is unknown.
%C A386562 See A386559 and A386560 for other images of the graphs.
%H A386562 Scott R. Shannon, <a href="/A386562/a386562.png">Image for n = 2</a>. The integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.
%F A386562 Sum of row n = A386560(n).
%e A386562 The table begins:
%e A386562 4;
%e A386562 44, 24, 4;
%e A386562 184, 216, 24;
%e A386562 560, 780, 56;
%e A386562 1456, 1844, 224, 12;
%e A386562 3100, 3788, 376, 24, 4;
%e A386562 5860, 7100, 1148, 156, 8;
%e A386562 9860, 12436, 1848, 164, 20, 4;
%e A386562 16044, 19732, 3100, 460, 16, 4;
%e A386562 24744, 29568, 5048, 516, 32, 12;
%e A386562 36780, 43472, 9608, 1400, 68, 20;
%e A386562 52296, 61244, 12628, 1784, 116, 16;
%e A386562 72492, 85672, 20424, 3792, 268, 16;
%e A386562 97812, 115000, 27796, 4820, 344, 24, 8;
%e A386562 129416, 151184, 35716, 6240, 532, 28;
%e A386562 167712, 195816, 46380, 7956, 644, 44;
%e A386562 .
%e A386562 .
%Y A386562 Cf. A386559 (vertices), A386560 (regions), A386561 (edges), A344938, A346446.
%K A386562 nonn,tabf
%O A386562 1,1
%A A386562 _Scott R. Shannon_, Jul 26 2025