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.

2, 12, 36, 86, 180, 330, 570, 918, 1408, 2058, 2946, 4054, 5502, 7278, 9430, 12006, 15174, 18846, 23268, 28338, 34172, 40806, 48546, 57174, 67022, 78006, 90324, 103910, 119276, 135978, 154722, 175226, 197686, 222098, 248790, 277462, 309050, 343086, 379858, 419182, 462106, 507678

Offset: 1

Author

Scott R. Shannon, Jan 15 2024

Keywords

• nonn

Links

• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8. Note that 5-gons are now present.
• Scott R. Shannon, Image for n = 15.

Crossrefs

Cf. A369176 (vertices), A369177 (edges), A369178 (k-gons), A306302, A306302, A368755, A290131.

Formula

a(n) = A369177(n) - A369176(n) + 1 by Euler's formula.