A371374 Place n equally spaced points around the circumference of a circle and then, for each pair of points, draw two distinct circles, whose radii are the same as the first circle, such that both points lie on their circumferences. The sequence gives the total number of regions formed.

1, 1, 9, 9, 51, 48, 211, 217, 612, 651, 1475, 1248, 3017, 3193, 5415, 5793, 9623, 9000, 15429, 15901, 23352, 24311, 34501, 33840, 49001, 50337, 67365, 69385, 91003, 87720, 120219, 123169, 155430, 159291, 198521, 198792, 250121, 256121, 310635, 317441, 382203, 382032, 465691, 473573

Offset: 1

Author

Scott R. Shannon, Mar 20 2024

Keywords

• nonn

Comments

See A371373 and A371254 for further information. The details of the number of regions with k sides is given in A371376.

Links

• Scott R. Shannon, Image for n = 3. In this and other images the initial circle and n points are shown in white for clarity.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 9.
• Scott R. Shannon, Image for n = 10.
• Scott R. Shannon, Image for n = 11.
• Scott R. Shannon, Image for n = 12.
• Scott R. Shannon, Image for n = 15.
• Scott R. Shannon, Image for n = 20.
• Scott R. Shannon, Image for n = 24.
• Scott R. Shannon, Image for n = 30.

Crossrefs

Cf. A371373 (vertices), A371375 (edges), A371376 (k-gons), A371377 (vertex crossings), A371254, A371253, A006533, A358782, A359046.

Formula

a(n) = A371375(n) - A371373(n) + 1 by Euler's formula.