%I #32 Sep 08 2022 08:45:37

%S 1,0,0,1,1,0,1,1,1,1,2,2,2,3,4,4,5,6,7,9,10,12,15,18,21,26,31,37,44,

%T 54,64,76,92,111,132,159,191,229,275,330,396,475,570,684,821,985,1182,

%U 1418,1703,2043,2451,2942,3531,4236,5084,6101,7321,8785,10543,12652,15182,18219,21864,26237,31485

%N Expansion of 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14) (a Salem polynomial).

%C 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

%H G. C. Greubel, <a href="/A143644/b143644.txt">Table of n, a(n) for n = 0..1000</a>

%H Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,0,0,-1,0,0,1,1,0,0,-1).

%F G.f.: 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14). - _Colin Barker_, Nov 03 2012

%F 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

%p 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

%t CoefficientList[Series[1/(1-x^3-x^4+x^7-x^10-x^11+x^14), {x, 0, 50}], x]

%o (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

%o (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

%o (Sage)

%o def A143644_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) ).list()

%o A143644_list(50) # _G. C. Greubel_, Dec 06 2019

%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

%K nonn,easy

%O 0,11

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 26 2008

%E New name from _Colin Barker_ and _Joerg Arndt_, Nov 03 2012