OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-5,2).
FORMULA
a(n) = a(n-1) - Sum_{k=2..n-1} k*a(n-k), with a(1) = a(2) = 2, a(3) = -2.
a(n) = 2*A106540(n).
From Colin Barker, Aug 25 2016: (Start)
a(n) = 3*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.
G.f.: 2*x*(1-x)^2/(1-3*x+5*x^2-2*x^3). (End)
MATHEMATICA
lst={2, 2, -2}; f[n_]:=With[{c=(Times@@@Thread[{lst, Range[Length[lst], 1, -1]}])}, Last[c]- Total[Most[c]]]; Do[AppendTo[lst, f[lst]], {40}]; lst (* Harvey P. Dale, Apr 17 2012 *)
PROG
(Magma) I:=[2, 2, -2]; [n le 3 select I[n] else 3*Self(n-1) - 5*Self(n-2) + 2*Self(n-3): n in [1..41]]; // G. C. Greubel, Sep 03 2021
(Sage)
def A106541_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2*x*(1-x)^2/(1-3*x+5*x^2-2*x^3) ).list()
a=A106541_list(41); a[1:] # G. C. Greubel, Sep 03 2021
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Alexandre Wajnberg, May 08 2005
EXTENSIONS
More terms from Harvey P. Dale, Apr 17 2012
STATUS
approved