OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A125199(n,n-1) for n>1.
From Arkadiusz Wesolowski, Dec 25 2011: (Start)
a(1) = -1, a(n) = a(n-1) + 8*n - 10.
a(n) = 2*a(n-1) - a(n-2) + 8 with a(1) = -1 and a(2) = 5.
G.f.: (1 - 4*x + 11*x^2)/(1 - x)^3. (End)
a(n) = A002943(n-1) - 1. - Arkadiusz Wesolowski, Feb 15 2012
E.g.f.: exp(x)*(1 - 2*x + 4*x^2). - Stefano Spezia, Oct 10 2022
Sum_{n>=1} 1/a(n) = sqrt(5)/10*(psi(1/4+sqrt(5)/4) - psi(1/4-sqrt(5)/4)) = -0.656213833... - R. J. Mathar, Apr 22 2024
MATHEMATICA
f[a_]:=4*a^2-6*a+1; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 14 2009 *)
PROG
(Magma) [4*n^2 - 6*n + 1: n in [1..60]]; // Vincenzo Librandi, Jul 11 2011
(PARI) a(n)=4*n^2-6*n+1 \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Reinhard Zumkeller, Nov 24 2006
STATUS
approved