OFFSET
0,2
COMMENTS
The entries are the coefficients in a family of Jacobsthal recurrences: a(n)=k*a(n-1)+(3-k)*a(n-2)+(2-2k)*a(n-3).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 2, 0, 0, -1).
FORMULA
From R. J. Mathar, Feb 25 2009: (Start)
a(n) = 2*a(n-3) - a(n-6).
G.f.: x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x+x^2)^2). (End)
EXAMPLE
The triples (k,3-k,2-2k) are (0,3,2), (1,2,0), (2,1,-2), (3,0,-4),...
MATHEMATICA
CoefficientList[Series[x*(3 + 2*x + x^2 - 4*x^3 - 4*x^4)/((x - 1)^2*(1 + x + x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 28 2017 *)
Table[{n, 3-n, 2-2n}, {n, 0, 30}]//Flatten (* or *) LinearRecurrence[ {0, 0, 2, 0, 0, -1}, {0, 3, 2, 1, 2, 0}, 100] (* Harvey P. Dale, Jun 23 2019 *)
PROG
(PARI) x='x+O('x^50); Vec(x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x +x^2 )^2)) \\ G. C. Greubel, Sep 28 2017
CROSSREFS
KEYWORD
easy,sign,less
AUTHOR
Paul Curtz, Mar 09 2008
EXTENSIONS
Edited by R. J. Mathar, Jun 28 2008
STATUS
approved