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A254527 Total number of points on a sphere when both poles are on an x by x grid where x=8*n+1.

%I A254527 #29 Feb 22 2024 20:22:28
%S A254527 6,26,62,114,182,266,366,482,614,762,926,1106,1302,1514,1742,1986,
%T A254527 2246,2522,2814,3122,3446,3786,4142,4514,4902,5306,5726,6162,6614,
%U A254527 7082,7566,8066,8582,9114,9662,10226,10806,11402,12014,12642,13286,13946,14622,15314
%N A254527 Total number of points on a sphere when both poles are on an x by x grid where x=8*n+1.
%C A254527 Maximum number of regions formed by n circles and n ellipses in the plane. - _Ivan N. Ianakiev_, Sep 21 2019
%C A254527 Number of points on a sphere whose longitude and latitude are both multiples of (90 degrees)/n, including the poles. - _Jianing Song_, Aug 28 2022
%H A254527 Colin Barker, <a href="/A254527/b254527.txt">Table of n, a(n) for n = 1..1000</a>
%H A254527 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A254527 a(n) = 8*n^2 - 4*n + 2.
%F A254527 From _Colin Barker_, Aug 09 2015: (Start)
%F A254527 a(n) = 2*A054554(n+1).
%F A254527 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A254527 G.f.: -2*x*(x+1)*(x+3) / (x-1)^3.
%F A254527 (End)
%F A254527 E.g.f.: -2 + exp(x)*(2 + 4*x + 8*x^2). - _Stefano Spezia_, Sep 21 2019
%F A254527 a(n) = A051890(2*n). - _Jianing Song_, Aug 28 2022
%t A254527 Table[8*n^2  - 4*n + 2,{n,1,44}] (* _Ivan N. Ianakiev_, Sep 21 2019 *)
%o A254527 (PARI) vector(50, n, 8*n^2 - 4*n + 2) \\ _Michel Marcus_, Feb 08 2015
%o A254527 (PARI) Vec(-2*x*(x+1)*(x+3)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Aug 09 2015
%Y A254527 Cf. A054554, A051890.
%K A254527 nonn,easy
%O A254527 1,1
%A A254527 _Thomas Olson_, Jan 31 2015