cp's OEIS Frontend

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.

%I A369178 #16 Jan 22 2024 08:58:11
%S A369178 2,8,4,22,14,52,34,98,82,184,146,302,268,484,426,8,710,694,4,1064,986,
%T A369178 8,1498,1436,12,2056,1986,12,2710,2780,12,3624,3630,24,4682,4728,20,
%U A369178 6012,5970,24,7518,7628,28,9408,9406,32,11526,11702,40,14028,14246,64,16782,17330,60
%N 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.
%C A369178 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 A369178 Scott R. Shannon, <a href="/A369178/a369178.png">Image for n = 7</a>.
%H A369178 Scott R. Shannon, <a href="/A369178/a369178_1.png">Image for n = 8</a>.
%F A369178 Sum of row(n) = A369175(n).
%e A369178 The table begins:
%e A369178 2;
%e A369178 8, 4;
%e A369178 22, 14;
%e A369178 52, 34;
%e A369178 98, 82;
%e A369178 184, 146;
%e A369178 302, 268;
%e A369178 484, 426, 8;
%e A369178 710, 694, 4;
%e A369178 1064, 986, 8;
%e A369178 1498, 1436, 12;
%e A369178 2056, 1986, 12;
%e A369178 2710, 2780, 12;
%e A369178 3624, 3630, 24;
%e A369178 4682, 4728, 20;
%e A369178 6012, 5970, 24;
%e A369178 7518, 7628, 28;
%e A369178 9408, 9406, 32;
%e A369178 11526, 11702, 40;
%e A369178 14028, 14246, 64;
%e A369178 16782, 17330, 60;
%e A369178 20220, 20518, 68;
%e A369178 23998, 24468, 80;
%e A369178 28304, 28786, 84;
%e A369178 .
%e A369178 .
%Y A369178 Cf. A369175 (regions), A369176 (vertices), A369177 (edges), A306302, A324042, A324043, A368758.
%K A369178 nonn,tabf
%O A369178 1,1
%A A369178 _Scott R. Shannon_, Jan 15 2024