A370980 If n is even, (n^2-2*n+2)/2, otherwise (n^2-n+2)/2.

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

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 * A379357 A039006 A191209

Adjacent sequences: A370977 A370978 A370979 * A370981 A370982 A370983

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, Mar 23 2024

Status

approved