A106542 a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - ... - (n-1)*a(1), a(1) = a(2) = 3, a(3) = -3.

3, 3, -3, -18, -33, -15, 84, 261, 333, -138, -1557, -3315, -2436, 6153, 24009, 36390, 1431, -129639, -323292, -318819, 400725, 2149686, 3807795, 1476405, -10310388, -30697599, -37588047, 20103078, 186854271, 384871329, 260548788, -769001739, -2840006499

Offset

1,1

Links

Colin Barker, 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) = 3, a(3) = -3.

a(n) = 3*A106540(n).

From Colin Barker, Dec 04 2015: (Start)

a(n) = 3*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.

G.f.: 3*x*(1-x)^2/(1-3*x+5*x^2-2*x^3). (End)

Mathematica

LinearRecurrence[{3, -5, 2}, {3, 3, -3}, 40] (* G. C. Greubel, Sep 03 2021 *)

Prog

(PARI) a=vector(40); a[1]=3; for(n=2, #a, a[n]=a[n-1]-sum(k=2, n-1, k*a[n-k])); a[1..#a] \\ Colin Barker, Dec 04 2015
(Magma) I:=[3, 3, -3]; [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 A106542_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 3*x*(1-x)^2/(1-3*x+5*x^2-2*x^3) ).list()
a=A106542_list(41); a[1:] # G. C. Greubel, Sep 03 2021

Crossrefs

Cf. A106540, A106541.

Sequence in context: A356388 A083562 A332860 * A342363 A229934 A239125

Adjacent sequences: A106539 A106540 A106541 * A106543 A106544 A106545

Keyword

easy,sign

Author

Alexandre Wajnberg, May 08 2005

Status

approved