OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1).
FORMULA
G.f.: (1 + 2*x^2)/((1-x)*(1-x^2-x^3)).
a(n) = a(n-2) + a(n-3) + 3. - Greg Dresden, May 18 2020
MAPLE
seq(coeff(series((1+2*x^2)/((1-x)*(1-x^2-x^3)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 26 2019
MATHEMATICA
CoefficientList[Series[(1+2*x^2)/((1-x)*(1-x^2-x^3)), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 0, -1}, {1, 1, 4, 5}, 41] (* G. C. Greubel, Sep 26 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+2*x^2)/((1-x)*(1-x^2-x^3))) \\ G. C. Greubel, Sep 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x^2)/((1-x)*(1-x^2-x^3)) )); // G. C. Greubel, Sep 26 2019
(Sage)
def A027975_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+2*x^2)/((1-x)*(1-x^2-x^3)) ).list()
A027975_list(40) # G. C. Greubel, Sep 26 2019
(GAP) a:=[1, 1, 4, 5];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]-a[n-4]; od; a; # G. C. Greubel, Sep 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(32) onward added by G. C. Greubel, Sep 26 2019
STATUS
approved