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A369178
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.
4
2, 8, 4, 22, 14, 52, 34, 98, 82, 184, 146, 302, 268, 484, 426, 8, 710, 694, 4, 1064, 986, 8, 1498, 1436, 12, 2056, 1986, 12, 2710, 2780, 12, 3624, 3630, 24, 4682, 4728, 20, 6012, 5970, 24, 7518, 7628, 28, 9408, 9406, 32, 11526, 11702, 40, 14028, 14246, 64, 16782, 17330, 60
OFFSET
1,1
COMMENTS
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.
LINKS
Scott R. Shannon, Image for n = 7.
Scott R. Shannon, Image for n = 8.
FORMULA
Sum of row(n) = A369175(n).
EXAMPLE
The table begins:
2;
8, 4;
22, 14;
52, 34;
98, 82;
184, 146;
302, 268;
484, 426, 8;
710, 694, 4;
1064, 986, 8;
1498, 1436, 12;
2056, 1986, 12;
2710, 2780, 12;
3624, 3630, 24;
4682, 4728, 20;
6012, 5970, 24;
7518, 7628, 28;
9408, 9406, 32;
11526, 11702, 40;
14028, 14246, 64;
16782, 17330, 60;
20220, 20518, 68;
23998, 24468, 80;
28304, 28786, 84;
.
.
CROSSREFS
Cf. A369175 (regions), A369176 (vertices), A369177 (edges), A306302, A324042, A324043, A368758.
Sequence in context: A264142 A088156 A019193 * A253884 A054788 A193851
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Jan 15 2024
STATUS
approved