A369175 - OEIS

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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.

4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..42.

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.

FORMULA

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

CROSSREFS

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

Sequence in context: A176583 A011379 A338610 * A073404 A141208 A181825

Adjacent sequences: A369172 A369173 A369174 * A369176 A369177 A369178

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Jan 15 2024

STATUS

approved