OFFSET
0,11
COMMENTS
Limiting ratio is 1.2000265239873915..., the largest real root of 1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14: 1.200026523987391518902962100414 is a candidate for the smallest degree-14 Salem number. The absolute values of the roots of the polynomial are 0.8333149143..., 1.200026523..., and 1.0 (with multiplicity 12). The polynomial is self-reciprocal. - Joerg Arndt, Nov 03 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,-1,0,0,1,1,0,0,-1).
FORMULA
G.f.: 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14). - Colin Barker, Nov 03 2012
a(n) = a(n-3) + a(n-4) - a(n-7) + a(n-10) + a(n-11) - a(n-14). - Franck Maminirina Ramaharo, Oct 30 2018
MAPLE
seq(coeff(series(1/(1-x^3-x^4+x^7-x^10-x^11+x^14), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 06 2019
MATHEMATICA
CoefficientList[Series[1/(1-x^3-x^4+x^7-x^10-x^11+x^14), {x, 0, 50}], x]
PROG
(PARI) my(x='x+O('x^50)); Vec(1/(1-x^3-x^4+x^7-x^10-x^11+x^14)) \\ G. C. Greubel, Dec 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) )); // G. C. Greubel, Dec 06 2019
(Sage)
def A143644_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) ).list()
A143644_list(50) # G. C. Greubel, Dec 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 26 2008
EXTENSIONS
New name from Colin Barker and Joerg Arndt, Nov 03 2012
STATUS
approved