OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-11,8).
FORMULA
a(n) = 6*a(n-1) - 11*a(n-2) + 8*a(n-3) with a(0)=1, a(1)=2 and a(2)= 5.
a(n) = Sum_{k=0..floor(n/2)} A013609(n+k,n-2*k).
G.f.: (1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3).
MAPLE
nmax:=24: a(0):=1: a(1):=2: a(2):=5: for n from 3 to nmax do a(n) := 6*a(n-1)-11*a(n-2)+8*a(n-3) od: seq(a(n), n=0..nmax);
MATHEMATICA
LinearRecurrence[{6, -11, 8}, {1, 2, 5}, 30] (* or *) CoefficientList[ Series[(1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3), {x, 0, 30}], x] (* G. C. Greubel, Jun 06 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3)) \\ G. C. Greubel, Jun 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3) )); // G. C. Greubel, Jun 06 2019
(Sage) ((1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019
(GAP) a:=[1, 2, 5];; for n in [4..30] do a[n]:=6*a[n-1]-11*a[n-2]+8*a[n-3]; od; a; # G. C. Greubel, Jun 06 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Sep 21 2010
STATUS
approved