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A143438 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6), with a(0) = a(2) = a(3) = 1, a(1) = 0 and a(4) = a(5) = 2.

%I A143438 #28 Sep 08 2022 08:45:37
%S A143438 1,0,1,1,2,2,3,5,6,9,12,18,24,34,48,67,94,131,185,258,362,507,711,996,
%T A143438 1395,1956,2740,3840,5380,7540,10565,14804,20745,29069,40734,57078,
%U A143438 79983,112077,157050,220069,308376,432118,605512,848486,1188956,1666047,2334578
%N A143438 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6), with a(0) = a(2) = a(3) = 1, a(1) = 0 and a(4) = a(5) = 2.
%C A143438 Expansion of 1/p(x), where p(x) = 1 - x^2 - x^3 - x^4 + x^6 is a Salem polynomial.
%H A143438 G. C. Greubel, <a href="/A143438/b143438.txt">Table of n, a(n) for n = 0..1000</a>
%H A143438 Curtis T. McMullen, <a href="http://abel.math.harvard.edu/~ctm/papers/index.html">Dynamics on K3 surfaces: Salem numbers and Siegel disks</a>, 2001.
%H A143438 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,0,-1).
%F A143438 G.f.: 1/(1 - x^2 - x^3 - x^4 + x^6). - _Colin Barker_, Nov 24 2012
%p A143438 seq(coeff(series(1/(1-x^2-x^3-x^4+x^6), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Dec 06 2019
%t A143438 CoefficientList[Series[1/(1-x^2-x^3-x^4+x^6), {x, 0, 50}], x]
%t A143438 LinearRecurrence[{0,1,1,1,0,-1}, {1,0,1,1,2,2}, 50] (* _G. C. Greubel_, Dec 06 2019 *)
%o A143438 (Maxima) makelist(ratcoef(taylor(1/(1 -x^2 -x^3 -x^4 +x^6), x, 0, n), x, n), n, 0, 50); /* _Franck Maminirina Ramaharo_, Oct 31 2018 */
%o A143438 (PARI) my(x='x+O('x^50)); Vec(1/(1-x^2-x^3-x^4+x^6)) \\ _G. C. Greubel_, Nov 03 2018
%o A143438 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^2-x^3-x^4+x^6))); // _G. C. Greubel_, Nov 03 2018
%o A143438 (Sage)
%o A143438 def A143438_list(prec):
%o A143438     P.<x> = PowerSeriesRing(ZZ, prec)
%o A143438     return P(1/(1-x^2-x^3-x^4+x^6)).list()
%o A143438 A143438_list(50) # _G. C. Greubel_, Dec 06 2019
%o A143438 (GAP) a:=[1,0,1,1,2,2];; for n in [7..50] do a[n]:=a[n-2]+a[n-3]+a[n-4]-a[n-6]; od; a; # _G. C. Greubel_, Dec 06 2019
%Y A143438 Cf. A029826, A117791, A143419, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K A143438 nonn,easy
%O A143438 0,5
%A A143438 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008
%E A143438 Edited, new name (after _Colin Barker_), more terms, and offset corrected by _Franck Maminirina Ramaharo_, Oct 30 2018