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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.
11
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Mar 20 2024
STATUS
approved