cp's OEIS Frontend

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

%I A370980 #29 Jul 07 2024 07:58:04
%S A370980 1,1,1,4,5,11,13,22,25,37,41,56,61,79,85,106,113,137,145,172,181,211,
%T A370980 221,254,265,301,313,352,365,407,421,466,481,529,545,596,613,667,685,
%U A370980 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
%N A370980 If n is even, (n^2-2*n+2)/2, otherwise (n^2-n+2)/2.
%C A370980 Total number of circles in A371373 and A371253, if in the later all the circular arcs are completed to form full circles.
%C A370980 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.
%H A370980 Scott R. Shannon, <a href="/A370980/a370980.jpg">Image for n = 3</a>. In this and other images the center of each circle of shown as a white dot.
%H A370980 Scott R. Shannon, <a href="/A370980/a370980_1.jpg">Image for n = 4</a>.
%H A370980 Scott R. Shannon, <a href="/A370980/a370980_2.jpg">Image for n = 5</a>
%H A370980 Scott R. Shannon, <a href="/A370980/a370980_3.jpg">Image for n = 10</a>.
%H A370980 Scott R. Shannon, <a href="/A370980/a370980_4.jpg">Image for n = 20</a>.
%F A370980 a(n) = A183207(n) - A093005(n) + 1, by Euler's formula. - _Scott R. Shannon_, Jul 07 2024
%e A370980 a(n) = 1+n*floor((n-1)/2) = 1+n*A004526(n-1). - _Chai Wah Wu_, Mar 23 2024
%o A370980 (Python)
%o A370980 def A370980(n): return n*(n-1>>1)+1 # _Chai Wah Wu_, Mar 23 2024
%Y A370980 Bisections are A001844 and A084849.
%Y A370980 Cf. A371373, A371374, A371375.
%Y A370980 Cf. A004526, A371253, A371254, A371253, A183297, A093005, A183207.
%K A370980 nonn
%O A370980 0,4
%A A370980 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 23 2024