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%I #32 Aug 18 2024 14:33:20
%S 1,-1,1,0,1,1,1,2,2,4,4,7,9,12,17,23,32,44,60,83,113,156,214,294,403,
%T 554,760,1044,1433,1967,2701,3708,5091,6988,9596,13172,18085,24828,
%U 34086,46797,64246,88203,121092,166246,228237,313343,430185,590594,810819
%N G.f.: 1/p(x), where p(x) = degree 22 Salem polynomial p(x) = x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1.
%H G. C. Greubel, <a href="/A143419/b143419.txt">Table of n, a(n) for n = 0..1000</a>
%H Curtis T. McMullen, <a href="http://abel.math.harvard.edu/~ctm/papers/home/text/papers/k3/k3.pdf">Dynamics on K3 surfaces: Salem numbers and Siegel disks</a>, 2001
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,2,3,3,2,0,-2,-4,-5,-4,-2,0,2,3,3,2,1,0,-1,-1).
%F a(n) = -a(n-1) + a(n-3) + 2*a(n-4) + 3*a(n-5) + 3*a(n-6) + 2*a(n-7) - 2*a(n-9) - 4*a(n-10) - 5*a(n-11) - 4*a(n-12) - 2*a(n-13) + 2*a(n-15) + 3*a(n-16) + 3*a(n-17) + 2*a(n-18) + a(n-19) - a(n-21) - a(n-22). - _Franck Maminirina Ramaharo_, Oct 30 2018
%t f[x_] = x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1;
%t CoefficientList[Series[1/f[x], {x, 0, 50}], x]
%t LinearRecurrence[{-1,0,1,2,3,3,2,0,-2,-4,-5,-4,-2,0,2,3,3,2,1,0,-1,-1},{1,-1,1,0,1,1,1,2,2,4,4,7,9,12,17,23,32,44,60,83,113,156},50] (* _Harvey P. Dale_, Aug 18 2024 *)
%o (PARI) p(x)=x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1; Vec(1/p(x)+O(x^60)) \\ _Charles R Greathouse IV_, Feb 13 2011
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(x^22 +x^21-x^19-2*x^18-3*x^17-3*x^16-2*x^15+2*x^13+4*x^12+5*x^11 + 4*x^10+2*x^9-2*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1))); // _G. C. Greubel_, Nov 03 2018
%Y Cf. A029826, A117791, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K easy,sign
%O 0,8
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008
%E Edited by _N. J. A. Sloane_, Dec 12 2008
%E More terms from _Sean A. Irvine_, Feb 13 2011
%E Offset corrected, and more terms from _Franck Maminirina Ramaharo_, Nov 02 2018