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

6, 26, 62, 114, 182, 266, 366, 482, 614, 762, 926, 1106, 1302, 1514, 1742, 1986, 2246, 2522, 2814, 3122, 3446, 3786, 4142, 4514, 4902, 5306, 5726, 6162, 6614, 7082, 7566, 8066, 8582, 9114, 9662, 10226, 10806, 11402, 12014, 12642, 13286, 13946, 14622, 15314

Offset

1,1

Comments

Maximum number of regions formed by n circles and n ellipses in the plane. - Ivan N. Ianakiev, Sep 21 2019

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 8*n^2 - 4*n + 2.

From Colin Barker, Aug 09 2015: (Start)

a(n) = 2*A054554(n+1).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

G.f.: -2*x*(x+1)*(x+3) / (x-1)^3.

(End)

E.g.f.: -2 + exp(x)*(2 + 4*x + 8*x^2). - Stefano Spezia, Sep 21 2019

a(n) = A051890(2*n). - Jianing Song, Aug 28 2022

Mathematica

Table[8*n^2  - 4*n + 2, {n, 1, 44}] (* Ivan N. Ianakiev, Sep 21 2019 *)

Prog

(PARI) vector(50, n, 8*n^2 - 4*n + 2) \\ Michel Marcus, Feb 08 2015
(PARI) Vec(-2*x*(x+1)*(x+3)/(x-1)^3 + O(x^100)) \\ Colin Barker, Aug 09 2015

Crossrefs

Cf. A054554, A051890.

Sequence in context: A285453 A327713 A136892 * A190095 A135036 A166796

Adjacent sequences: A254524 A254525 A254526 * A254528 A254529 A254530

Keyword

nonn,easy

Author

Thomas Olson, Jan 31 2015

Status

approved