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A173911 Expansion of 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).

%I A173911 #25 Apr 02 2024 12:57:59
%S A173911 1,1,0,0,1,1,1,1,1,1,2,2,2,3,4,4,5,6,7,8,10,12,14,16,19,23,28,33,39,
%T A173911 46,55,66,78,92,110,131,155,184,219,260,309,368,437,519,617,733,871,
%U A173911 1036,1231,1462,1737,2065,2454,2916,3465,4118,4894,5816,6911,8213
%N A173911 Expansion of 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).
%C A173911 Limiting ratio is 1.188368147508223588... = A219300.
%H A173911 G. C. Greubel, <a href="/A173911/b173911.txt">Table of n, a(n) for n = 0..1000</a>
%H A173911 Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A173911 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,0,0,1,-1,1,-1,1,-1,1,0,0,1,-1,1,-1).
%F A173911 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
%p A173911 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
%t A173911 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]
%t A173911 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 *)
%o A173911 (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
%o A173911 (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
%o A173911 (Sage)
%o A173911 def A173911_list(prec):
%o A173911     P.<x> = PowerSeriesRing(ZZ, prec)
%o A173911     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()
%o A173911 A173911_list(50) # _G. C. Greubel_, Dec 15 2019
%Y A173911 Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K A173911 nonn,easy
%O A173911 0,11
%A A173911 _Roger L. Bagula_, Nov 26 2010