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A143335
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G.f. ( 1-2*x^3-2*x^5-x^8-x^4-x^6+2*x^9-x^7 ) / ( 1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10 ).
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1
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1, -1, 1, -2, 1, -2, 0, -1, -3, 2, -6, 1, -4, -3, -3, -5, -4, -7, -6, -9, -8, -14, -10, -18, -18, -20, -28, -27, -38, -39, -50, -57, -67, -79, -94, -109, -128, -154, -175, -213, -244, -292, -341, -400, -475, -553, -655, -768, -905, -1062, -1253
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Shares the same 10-th order "Salem" linear recurrence with A029826, A173243 and A125950.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,0,1,1,1,1,1,0,-1,-1).
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MATHEMATICA
| (* generate matrix using A087612*) 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 = CompanionMatrix[x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1, x]; (* generate starting vector :v(0)=A029826(n), n{1, 10); *) f[x_] = x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1; g[x] = ExpandAll[x^10*f[1/x]]; a = Table[SeriesCoefficient[Series[1/ g[x], {x, 0, 30}], n], {n, 0, 30}]; v[0] = Table[a[[n]], {n, 1, 10}]; v[n_] := v[n] = M.v[n - 1]; Table[v[n][[1]], {n, 0, 50}]
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CROSSREFS
| Cf. A087612, A125950, A029826, A070178.
Sequence in context: A190491 A143352 A127170 * A099505 A156837 A129559
Adjacent sequences: A143332 A143333 A143334 * A143336 A143337 A143338
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KEYWORD
| sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 22 2008
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EXTENSIONS
| Edited by Assoc. Eds. of the OEIS - Jun 30 2010
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