A331454 -id:A331454 - cp's OEIS frontend

A332609 Maximum number of edges in any cell in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

4, 4, 5, 5, 5, 6, 5, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 12 2020

nonn

See A331452 (the illustrations for T(n,2)) for pictures of these graphs.

Scott R. Shannon, Data specifically for nX2 (or 2Xn) rectangles

Cf. A331452, A331453, A331454, A331763, A331765, A331766, A332599, A332600, A331457, A332606, A332607, A332608.

a(21)-a(87) from Lars Blomberg, Apr 28 2020

A337229 Irregular table read by rows: row n gives the number of 3-gon to k-gon contacts, with k>=3, for an n X 2 grid of congruent rectangles divided by drawing diagonals of all possible rectangles (cf. A335701).

Original entry on oeis.org

14, 8, 56, 24, 88, 104, 16, 156, 204, 48, 208, 460, 88, 328, 760, 116, 24, 498, 1088, 304, 716, 1608, 492, 24, 894, 2632, 420, 0, 24, 20, 1282, 3436, 756, 108, 1730, 4780, 852, 104, 2156, 6332, 1348, 136, 2844, 8236, 1632, 152, 3594, 10464, 2388, 148, 4432, 13632, 2260, 404

Offset: 1

Scott R. Shannon, Aug 20 2020

See A335701 for other images of the n X 2 grid of congruent rectangles.

			The table begins:
.
14, 8;
56, 24;
88, 104, 16;
156, 204, 48;
208, 460, 88;
328, 760, 116, 24;
498, 1088, 304;
716, 1608, 492, 24;
894, 2632, 420, 0, 24, 20;
1282, 3436, 756, 108;
1730, 4780, 852, 104;
2156, 6332, 1348, 136;
2844, 8236, 1632, 152;
3594, 10464, 2388, 148;
4432, 13632, 2260, 404;
5530, 16604, 3354, 256;
6812, 20700, 3668, 280;

Scott R. Shannon, Image for n=1 with edge-count coloring. This is the first n-gon with 3-gon to 3-gon and 3-gon to 4-gon contacts.
Scott R. Shannon, Image for n=3 with edge-count coloring. This is the first n-gon with 3-gon to 5-gon contacts.
Scott R. Shannon, Image for n=6 with edge-count coloring. This is the first n-gon with 3-gon to 6-gon contacts.
Scott R. Shannon, Image for n=9 with edge-count coloring. This is the first n-gon with 3-gon to 7-gon and 3-gon to 8-gon contacts.

Cf. A335701, A331454, A331766, A331763, A336731.

cp's OEIS Frontend

A332609 Maximum number of edges in any cell in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

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