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
KEYWORD
nonn,easy
AUTHOR
Thomas Olson, Jan 31 2015
STATUS
approved