OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003947, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 21474836470, A003947(17) = 21474836480. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-6).
FORMULA
G.f.: (t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1) / (6*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
G.f.: (1+t)*(1-t^17)/(1 -4*t +9*t^17 -6*t^18). - G. C. Greubel, Feb 22 2021
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^17)/(1 -4*t +9*t^17 -6*t^18), {t, 0, 40}], t] (* G. C. Greubel, Aug 03 2016, Feb 22 2021 *)
coxG[{17, 6, -3, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Feb 22 2021 *)
PROG
(PARI) Vec(Pol(vector(18, i, if(i<2||i>17, 1, 2))) / Pol(vector(18, i, if(i<2, 6, i>17, 1, -3)))+O(x^99)) \\ Charles R Greathouse IV, Aug 03 2016
(Magma)
R<t>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -4*t +9*t^17 -6*t^18) )); // G. C. Greubel, Feb 22 2021
(Sage)
def A168682_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^17)/(1 -4*t +9*t^17 -6*t^18) ).list()
A168682_list(40) # G. C. Greubel, Feb 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved