Search: id:A143611
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%I A143611
%S A143611 1,1,2,3,4,6,8,11,14,18,23,29,36,45,55,67,82,99,120,144,173,207,247,295,
%T A143611 351,417,495,587,695,823,973,1150,1358,1603,1892,2231,2631,3101,3654,
%U A143611 4305,5071,5972,7032,8279,9746,11472,13502,15891,18700,22005,25893
%N A143611 Coefficient expansion sequence of symmetric polynomial: p(x)=1 - x - 
               x^2 + x^4 + x^8 - x^10 - x^11 + x^12.
%C A143611 A factor of Lehmer's polynomial from a 12th degree symmetrical polynomial 
               census:(x-1)^2 times Lehmer's polynomial.
%C A143611 Vector matrix Markov that gives the same sequence is:
%C A143611 CompanionMatrix[p_, x_] := Module[{cl = CoefficientList[p, x], deg,
%C A143611 m}, cl = Drop[cl/Last[cl], -1]; deg = Length[cl]; If[deg == 1, {-cl},
%C A143611 m = RotateLeft[IdentityMatrix[deg]]; m[[ -1]] = -cl; Transpose[m]]];
%C A143611 M = Transpose[CompanionMatrix[1 - x - x^2 + x^4 + x^8 - x^10 - x^11 + 
               x^12, x]];
%C A143611 v[0] = Table[a[[n]], {n, 1, 12}];
%C A143611 v[n_] := v[n] = M.v[n - 1];
%C A143611 Table[v[n][[1]], {n, 0, 50}]
%F A143611 p(x)=1 - x - x^2 + x^4 + x^8 - x^10 - x^11 + x^12; a(n)=Coefficient_expansion(x^12*p(1/
               x))
%F A143611 G.f.: x/((1-x)^2(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10)). [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Nov 01 2008]
%t A143611 f[x_] = 1 - x - x^2 + x^4 + x^8 - x^10 - x^11 + x^12; g[x] = ExpandAll[x^12*f[1/
               x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], 
               {n, 0, 50}];
%Y A143611 Sequence in context: A114829 A007279 A034891 this_sequence A062464 A053270 
               A003412
%Y A143611 Adjacent sequences: A143608 A143609 A143610 this_sequence A143612 A143613 
               A143614
%K A143611 nonn
%O A143611 1,3
%A A143611 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 
               26 2008

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