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

Author

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

Keywords

• nonn

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.

Examples

			a(n) = 1+n*floor((n-1)/2) = 1+n*A004526(n-1). - _Chai Wah Wu_, Mar 23 2024
		

Links

• 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.

Crossrefs

Bisections are A001844 and A084849.

Cf. A371373, A371374, A371375.

Cf. A004526, A371253, A371254, A371253, A183297, A093005, A183207.

Programs

Python

def A370980(n): return n*(n-1>>1)+1 # Chai Wah Wu, Mar 23 2024

Formula

a(n) = A183207(n) - A093005(n) + 1, by Euler's formula. - Scott R. Shannon, Jul 07 2024