OFFSET
0,11
COMMENTS
Limiting ratio is 1.188368147508223588... = A219300.
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 (1,-1,1,0,0,1,-1,1,-1,1,-1,1,0,0,1,-1,1,-1).
FORMULA
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) - a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) + a(n-15) - a(n-16) + a(n-17) - a(n-16). - Franck Maminirina Ramaharo, Nov 02 2018
MAPLE
seq(coeff(series(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 15 2019
MATHEMATICA
CoefficientList[Series[1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), {x, 0, 50}], x]
LinearRecurrence[{1, -1, 1, 0, 0, 1, -1, 1, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1}, {1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6}, 60] (* Harvey P. Dale, Apr 02 2024 *)
PROG
(PARI) my(x='x+O('x^50)); Vec(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+ x^16-x^17+x^18)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16-x^17+x^18))); // G. C. Greubel, Nov 03 2018
(Sage)
def A173911_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18) ).list()
A173911_list(50) # G. C. Greubel, Dec 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 26 2010
STATUS
approved