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
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
Table[8*n^2 - 4*n + 2,{n,1,44}] (* Ivan N. Ianakiev, Sep 21 2019 *) -
PARI
vector(50, n, 8*n^2 - 4*n + 2) \\ Michel Marcus, Feb 08 2015
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PARI
Vec(-2*x*(x+1)*(x+3)/(x-1)^3 + O(x^100)) \\ Colin Barker, Aug 09 2015
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
Comments