cp's OEIS Frontend

A369175 Number of regions 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 A369175 #20 Jan 22 2024 08:58:37
%S A369175 2,12,36,86,180,330,570,918,1408,2058,2946,4054,5502,7278,9430,12006,
%T A369175 15174,18846,23268,28338,34172,40806,48546,57174,67022,78006,90324,
%U A369175 103910,119276,135978,154722,175226,197686,222098,248790,277462,309050,343086,379858,419182,462106,507678
%N A369175 Number of regions 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.
%H A369175 Scott R. Shannon, <a href="/A369175/a369175.png">Image for n = 2</a>.
%H A369175 Scott R. Shannon, <a href="/A369175/a369175_1.png">Image for n = 4</a>.
%H A369175 Scott R. Shannon, <a href="/A369175/a369175_2.png">Image for n = 7</a>.
%H A369175 Scott R. Shannon, <a href="/A369175/a369175_3.png">Image for n = 8</a>. Note that 5-gons are now present.
%H A369175 Scott R. Shannon, <a href="/A369175/a369175_5.png">Image for n = 15</a>.
%F A369175 a(n) = A369177(n) - A369176(n) + 1 by Euler's formula.
%Y A369175 Cf. A369176 (vertices), A369177 (edges), A369178 (k-gons), A306302, A306302, A368755, A290131.
%K A369175 nonn
%O A369175 1,1
%A A369175 _Scott R. Shannon_, Jan 15 2024