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Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, in a graph of n adjacent rectangles in a row with all possible diagonals drawn, as in A306302, but without the rectangles' edges which are perpendicular to the row.
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%I #16 Jan 22 2024 08:58:11

%S 2,8,4,22,14,52,34,98,82,184,146,302,268,484,426,8,710,694,4,1064,986,

%T 8,1498,1436,12,2056,1986,12,2710,2780,12,3624,3630,24,4682,4728,20,

%U 6012,5970,24,7518,7628,28,9408,9406,32,11526,11702,40,14028,14246,64,16782,17330,60

%N Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, in a graph of n adjacent rectangles in a row with all possible diagonals drawn, as in A306302, but without the rectangles' edges which are perpendicular to the row.

%C Unlike the graph in A306302, or the complete bipartite graph of order n, for n>=8 the graph contains regions with 5 edges. It is likely 5 is the maximum number of edges in any region for all n.

%H Scott R. Shannon, <a href="/A369178/a369178.png">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A369178/a369178_1.png">Image for n = 8</a>.

%F Sum of row(n) = A369175(n).

%e The table begins:

%e 2;

%e 8, 4;

%e 22, 14;

%e 52, 34;

%e 98, 82;

%e 184, 146;

%e 302, 268;

%e 484, 426, 8;

%e 710, 694, 4;

%e 1064, 986, 8;

%e 1498, 1436, 12;

%e 2056, 1986, 12;

%e 2710, 2780, 12;

%e 3624, 3630, 24;

%e 4682, 4728, 20;

%e 6012, 5970, 24;

%e 7518, 7628, 28;

%e 9408, 9406, 32;

%e 11526, 11702, 40;

%e 14028, 14246, 64;

%e 16782, 17330, 60;

%e 20220, 20518, 68;

%e 23998, 24468, 80;

%e 28304, 28786, 84;

%e .

%e .

%Y Cf. A369175 (regions), A369176 (vertices), A369177 (edges), A306302, A324042, A324043, A368758.

%K nonn,tabf

%O 1,1

%A _Scott R. Shannon_, Jan 15 2024