OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (-2,-1).
FORMULA
From R. J. Mathar, Aug 27 2009: (Start)
a(n) = -2*a(n-1)-a(n-2), n>3.
G.f.: (1+3*x^2)/(1+x)^2.
a(n) = 4*(-1)^n*n+2*(-1)^(n+1) = (-1)^n*A016825(n-1), n>0. (End)
E.g.f.: 3 - 2*exp(-x)*(1 + 2*x). - Stefano Spezia, Feb 02 2023
MATHEMATICA
CoefficientList[Series[(1+3*x^2)/(1+x)^2, {x, 0, 80}], x] (* or *) LinearRecurrence[ {-2, -1}, {1, -2, 6}, 80] (* Harvey P. Dale, Mar 19 2016 *)
PROG
(PARI) x='x+O('x^99); Vec((1+3*x^2)/(1+x)^2) \\ Altug Alkan, Apr 17 2018
(Python)
def A161718(n): return (2-(n<<2) if n&1 else (n<<2)-2) if n else 1 # Chai Wah Wu, Oct 12 2025
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Pr Mosbah Amlouk (Mosbah.Amlouk(AT)fsb.rnu.tn), Jun 17 2009
EXTENSIONS
Spurious commas in sequence deleted by N. J. A. Sloane, Aug 02 2009
Offset corrected, extended by R. J. Mathar, Aug 27 2009
Edited by Joerg Arndt, Sep 04 2011
STATUS
approved