OFFSET
0,5
COMMENTS
Expansion of 1/p(x), where p(x) = 1 - x^2 - x^3 - x^4 + x^6 is a Salem polynomial.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Curtis T. McMullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, 2001.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,0,-1).
FORMULA
G.f.: 1/(1 - x^2 - x^3 - x^4 + x^6). - Colin Barker, Nov 24 2012
MAPLE
seq(coeff(series(1/(1-x^2-x^3-x^4+x^6), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 06 2019
MATHEMATICA
CoefficientList[Series[1/(1-x^2-x^3-x^4+x^6), {x, 0, 50}], x]
LinearRecurrence[{0, 1, 1, 1, 0, -1}, {1, 0, 1, 1, 2, 2}, 50] (* G. C. Greubel, Dec 06 2019 *)
PROG
(Maxima) makelist(ratcoef(taylor(1/(1 -x^2 -x^3 -x^4 +x^6), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Oct 31 2018 */
(PARI) my(x='x+O('x^50)); Vec(1/(1-x^2-x^3-x^4+x^6)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^2-x^3-x^4+x^6))); // G. C. Greubel, Nov 03 2018
(Sage)
def A143438_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(1/(1-x^2-x^3-x^4+x^6)).list()
A143438_list(50) # G. C. Greubel, Dec 06 2019
(GAP) a:=[1, 0, 1, 1, 2, 2];; for n in [7..50] do a[n]:=a[n-2]+a[n-3]+a[n-4]-a[n-6]; od; a; # G. C. Greubel, Dec 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 23 2008
EXTENSIONS
Edited, new name (after Colin Barker), more terms, and offset corrected by Franck Maminirina Ramaharo, Oct 30 2018
STATUS
approved