A106541 a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - ... - (n-1)*a(1), with a(1) = a(2) = 2, a(3) = -2.

2, 2, -2, -12, -22, -10, 56, 174, 222, -92, -1038, -2210, -1624, 4102, 16006, 24260, 954, -86426, -215528, -212546, 267150, 1433124, 2538530, 984270, -6873592, -20465066, -25058698, 13402052, 124569514, 256580886, 173699192, -512667826, -1893337666

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

Cf. A106540, A106542.

Sequence in context: A335986 A152662 A135322 * A077945 A077991 A336491

Adjacent sequences: A106538 A106539 A106540 * A106542 A106543 A106544

Keyword

easy,sign

Author

Alexandre Wajnberg, May 08 2005

Extensions

More terms from Harvey P. Dale, Apr 17 2012

Status

approved