OFFSET
0,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,-3,-1).
FORMULA
a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) - a(n-4).
G.f.: x*(1-2*x^2) / ( 1-2*x-2*x^2+3*x^3+x^4 ). - R. J. Mathar, May 08 2014
MATHEMATICA
(See A192922.)
CoefficientList[Series[x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4), {x, 0, 30}], x] (* G. C. Greubel, Jun 26 2017 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4) )) \\ G. C. Greubel, Jun 26 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4) )); // G. C. Greubel, Feb 06 2019
(Sage) (x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Feb 06 2019
(GAP) a:=[0, 1, 2, 4];; for n in [5..30] do a[n]:=2*a[n-1]+2*a[n-2]-3*a[n-3] -a[n-4]; od; a; # G. C. Greubel, Feb 06 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 12 2011
STATUS
approved