OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1005
Index entries for linear recurrences with constant coefficients, signature (3,0,-2,1).
FORMULA
G.f.: (1 - x)^2/(1 - 3*x + 2*x^3 - x^4).
a(n) = 3*a(n-1) - 2*a(n-3) + a(n-4).
a(n) = Sum_{alpha=RootOf(-1+3*z-2*z^3+z^4)} (1/643)*(79 + 128*alpha - 133*alpha^2 + 40*alpha^3)*alpha^(-1-n).
MAPLE
spec := [S, {S=Sequence(Prod(Union(Prod(Sequence(Z), Sequence(Z)), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq(coeff(series((1-x)^2/(1-3*x+2*x^3-x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 21 2019
MATHEMATICA
LinearRecurrence[{3, 0, -2, 1}, {1, 1, 4, 10}, 30] (* G. C. Greubel, Oct 21 2019 *)
CoefficientList[Series[(1-x)^2/(1-3x+2x^3-x^4), {x, 0, 30}], x] (* Harvey P. Dale, Aug 30 2020 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-x)^2/(1-3*x+2*x^3-x^4)) \\ G. C. Greubel, Oct 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)^2/(1-3*x+2*x^3-x^4) )); // G. C. Greubel, Oct 21 2019
(Sage)
def A052946_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x)^2/(1-3*x+2*x^3-x^4)).list()
A052946_list(30) # G. C. Greubel, Oct 21 2019
(GAP) a:=[1, 1, 4, 10];; for n in [5..30] do a[n]:=3*a[n-1]-2*a[n-3]+a[n-4]; od; a; # G. C. Greubel, Oct 21 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 06 2000
STATUS
approved