A371374 Place n equally space 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

1,3

Comments

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

Links

Table of n, a(n) for n=1..44.

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.

Formula

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

Crossrefs

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

Sequence in context: A095344 A141635 A014718 * A339324 A145971 A241868

Adjacent sequences: A371371 A371372 A371373 * A371375 A371376 A371377

Keyword

nonn

Author

Scott R. Shannon, Mar 20 2024

Status

approved