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 A370980 If n is even, (n^2-2*n+2)/2, otherwise (n^2-n+2)/2. 6
 1, 1, 1, 4, 5, 11, 13, 22, 25, 37, 41, 56, 61, 79, 85, 106, 113, 137, 145, 172, 181, 211, 221, 254, 265, 301, 313, 352, 365, 407, 421, 466, 481, 529, 545, 596, 613, 667, 685, 742, 761, 821, 841, 904, 925, 991, 1013, 1082, 1105, 1177, 1201, 1276, 1301, 1379, 1405, 1486, 1513, 1597, 1625, 1712, 1741, 1831, 1861, 1954 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Total number of circles in A371373 and A371253, if in the later all the circular arcs are completed to form full circles. The sequence also gives the number of vertices created from circle intersections when a circle of radius r is drawn around each of n equally spaced points on the circumference of a circle of radius r. The number of regions in these constructions is A093005(n) and the number of edges is A183207(n). See the attached images. - Scott R. Shannon, Jul 06 2024. LINKS Table of n, a(n) for n=0..63. Scott R. Shannon, Image for n = 3. In this and other images the center of each circle of shown as a white dot. Scott R. Shannon, Image for n = 4. Scott R. Shannon, Image for n = 5 Scott R. Shannon, Image for n = 10. Scott R. Shannon, Image for n = 20. FORMULA a(n) = A183207(n) - A093005(n) + 1, by Euler's formula. - Scott R. Shannon, Jul 07 2024 EXAMPLE a(n) = 1+n*floor((n-1)/2) = 1+n*A004526(n-1). - Chai Wah Wu, Mar 23 2024 PROG (Python) def A370980(n): return n*(n-1>>1)+1 # Chai Wah Wu, Mar 23 2024 CROSSREFS Bisections are A001844 and A084849. Cf. A371373, A371374, A371375. Cf. A004526, A371253, A371254, A371253, A183297, A093005, A183207. Sequence in context: A163098 A216562 A174009 * A039006 A191209 A262901 Adjacent sequences: A370977 A370978 A370979 * A370981 A370982 A370983 KEYWORD nonn AUTHOR Scott R. Shannon and N. J. A. Sloane, Mar 23 2024 STATUS approved

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Last modified August 11 23:39 EDT 2024. Contains 375081 sequences. (Running on oeis4.)