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A143611
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Coefficient expansion sequence of symmetric polynomial: p(x)=1 - x - x^2 + x^4 + x^8 - x^10 - x^11 + x^12.
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0
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1, 1, 2, 3, 4, 6, 8, 11, 14, 18, 23, 29, 36, 45, 55, 67, 82, 99, 120, 144, 173, 207, 247, 295, 351, 417, 495, 587, 695, 823, 973, 1150, 1358, 1603, 1892, 2231, 2631, 3101, 3654, 4305, 5071, 5972, 7032, 8279, 9746, 11472, 13502, 15891, 18700, 22005, 25893
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A factor of Lehmer's polynomial from a 12th degree symmetrical polynomial census:(x-1)^2 times Lehmer's polynomial.
Vector matrix Markov that gives the same sequence is:
CompanionMatrix[p_, x_] := Module[{cl = CoefficientList[p, x], deg,
m}, cl = Drop[cl/Last[cl], -1]; deg = Length[cl]; If[deg == 1, {-cl},
m = RotateLeft[IdentityMatrix[deg]]; m[[ -1]] = -cl; Transpose[m]]];
M = Transpose[CompanionMatrix[1 - x - x^2 + x^4 + x^8 - x^10 - x^11 + x^12, x]];
v[0] = Table[a[[n]], {n, 1, 12}];
v[n_] := v[n] = M.v[n - 1];
Table[v[n][[1]], {n, 0, 50}]
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FORMULA
| 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))
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]
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MATHEMATICA
| 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}];
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CROSSREFS
| Sequence in context: A175869 A007279 A034891 * A062464 A053270 A003412
Adjacent sequences: A143608 A143609 A143610 * A143612 A143613 A143614
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 26 2008
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