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.

4, 44, 24, 4, 184, 216, 24, 560, 780, 56, 1456, 1844, 224, 12, 3100, 3788, 376, 24, 4, 5860, 7100, 1148, 156, 8, 9860, 12436, 1848, 164, 20, 4, 16044, 19732, 3100, 460, 16, 4, 24744, 29568, 5048, 516, 32, 12, 36780, 43472, 9608, 1400, 68, 20, 52296, 61244, 12628, 1784, 116, 16

Offset: 1

Author

Scott R. Shannon, Jul 26 2025

Keywords

• nonn
• tabf

Comments

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.

See A386559 and A386560 for other images of the graphs.

Examples

			The table begins:
4;
44, 24, 4;
184, 216, 24;
560, 780, 56;
1456, 1844, 224, 12;
3100, 3788, 376, 24, 4;
5860, 7100, 1148, 156, 8;
9860, 12436, 1848, 164, 20, 4;
16044, 19732, 3100, 460, 16, 4;
24744, 29568, 5048, 516, 32, 12;
36780, 43472, 9608, 1400, 68, 20;
52296, 61244, 12628, 1784, 116, 16;
72492, 85672, 20424, 3792, 268, 16;
97812, 115000, 27796, 4820, 344, 24, 8;
129416, 151184, 35716, 6240, 532, 28;
167712, 195816, 46380, 7956, 644, 44;
.
.
		

Links

• Scott R. Shannon, Image for n = 2. The integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.

Crossrefs

Cf. A386559 (vertices), A386560 (regions), A386561 (edges), A344938, A346446.

Formula

Sum of row n = A386560(n).