OFFSET
0,2
COMMENTS
72*a(n) - 71 = (18*n+1)^2 = A161705(n)^2 is a perfect square. - Klaus Purath, Jan 14 2022
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Nickolas Arustamyan, Christopher Cox, Erik Lundberg, Sean Perry, and Zvi Rosen, On the Number of Equilibria Balancing Newtonian Point Masses with a Central Force, arXiv:2106.11416 [math-ph], 2021.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + 9*n - 4 (with a(0)=1). - Vincenzo Librandi, Nov 18 2010
From Klaus Purath, Jan 14 2022: (Start)
a(n) = A276819(n) + n.
From Stefano Spezia, Dec 25 2022: (Start)
O.g.f.: (1 + 3*x+ 5*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(2 + 10*x + 9*x^2)/2. (End)
MATHEMATICA
Table[1+n/2+9 n^2/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 6, 20}, 40] (* Harvey P. Dale, Oct 05 2012 *)
PROG
(PARI) a(n)=1+n/2+9*n^2/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved