OFFSET
0,1
COMMENTS
This sequence resembles the Perrin sequence, A001608. Like many such sequences with a(1)=0, any prime p divides a(p). The first pseudoprime (composite n divides a(n)) is 121.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,-1,-1).
FORMULA
a(n) = - trace({{0, 0, -1}, {1, 0, -1}, {0, 1, 0}})^n. - Artur Jasinski, Jan 10 2007
From R. J. Mathar, Oct 24 2009: (Start)
G.f.: -(3+x^2)/(1+x^2+x^3).
MAPLE
A112455 := proc(n)
option remember ;
if n <= 2 then
op(n+1, [-3, 0, 2]) ;
else
-procname(n-2)-procname(n-3) ;
end if;
end proc: # R. J. Mathar, Feb 18 2024
MATHEMATICA
Table[ -Tr[MatrixPower[{{0, 0, -1}, {1, 0, -1}, {0, 1, 0}}, n]], {n, 1, 60}] (* Artur Jasinski, Jan 10 2007 *)
LinearRecurrence[{0, -1, -1}, {-3, 0, 2}, 60] (* G. C. Greubel, May 19 2019 *)
PROG
(PARI) Vec(-(3+x^2)/(1+x^2+x^3)+O(x^60)) \\ Charles R Greathouse IV, May 15 2013
(Magma) I:=[-3, 0, 2]; [n le 3 select I[n] else -Self(n-2) -Self(n-3): n in [1..60]]; // G. C. Greubel, May 19 2019
(Sage) (-(3+x^2)/(1+x^2+x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, May 19 2019
(GAP) a:=[-3, 0, 2];; for n in [4..60] do a[n]:=-a[n-2]-a[n-3]; od; a; # G. C. Greubel, May 19 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Anthony C Robin, Dec 13 2005
EXTENSIONS
Edited by Don Reble, Jan 25 2006
STATUS
approved