OFFSET
4,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1003
Index entries for linear recurrences with constant coefficients, signature (4,-5,2,-1,2,-1).
FORMULA
From Colin Barker, Feb 19 2016: (Start)
a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -a(n-4) +2*a(n-5) -a(n-6) for n>9.
G.f.: x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)).
(End)
a(n) = A001590(n+5) -n*(5+n), n>=4. - R. J. Mathar, Jun 15 2020
MAPLE
seq(coeff(series(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)), x, n+1), x, n), n = 4..40); # G. C. Greubel, Nov 06 2019
MATHEMATICA
LinearRecurrence[{4, -5, 2, -1, 2, -1}, {1, 18, 59, 146, 319, 652}, 40] (* G. C. Greubel, Nov 06 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 06 2019
(Sage)
def A027053_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))).list()
a=A027053_list(40); a[4:] # G. C. Greubel, Nov 06 2019
(GAP) a:=[1, 18, 59, 146, 319, 652];; for n in [7..40] do a[n]:=4*a[n-1] -5*a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Nov 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved