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
KEYWORD
easy,sign
AUTHOR
Alexandre Wajnberg, May 08 2005
STATUS
approved