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A143351
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Expansion of x / ( 1-x^2-x^4-x^7-x^8-x^9-x^10 )
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0
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1, 0, 1, 0, 2, 0, 3, 1, 6, 3, 11, 7, 20, 15, 37, 32, 70, 68, 134, 141, 257, 288, 495, 583, 959, 1175, 1867, 2358, 3646, 4714, 7136, 9397, 13994, 18695, 27489, 37138, 54068, 73687, 106450, 146066, 209740, 289328, 413506, 572784, 815628, 1133455, 1609405
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OFFSET
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1,5
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COMMENTS
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A polynomial expansion sequence based on the Weaver telegraphic Polynomial: ( compare A122762): p(x)=-1 - x - x^2 - x^3 - x^6 - x^8 + x^10.
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REFERENCES
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Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38:
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LINKS
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Table of n, a(n) for n=1..47.
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,0,1,1,1,1).
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FORMULA
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p(x)=Expand[x^10*Det[{{-1, (1/x^4 + 1/x^2)}, {(1/x^6 + 1/x^5), 1/x^2 + 1/x^4 - 1}}]]; p(x)=-1 - x - x^2 - x^3 - x^6 - x^8 + x^10; a(n)==coefficient_expansion(x^10*p(1/x)).
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MATHEMATICA
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f[x_] = -1 - x - x^2 - x^3 - x^6 - x^8 + x^10; g[x] = ExpandAll[x^10*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]
CoefficientList[Series[x/(1-x^2-x^4-x^7-x^8-x^9-x^10), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, 0, 1, 1, 1, 1}, {0, 1, 0, 1, 0, 2, 0, 3, 1, 6}, 60] (* Harvey P. Dale, Mar 05 2016 *)
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CROSSREFS
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Cf. A122762.
Sequence in context: A130627 A006209 A005307 * A241644 A241640 A158449
Adjacent sequences: A143348 A143349 A143350 * A143352 A143353 A143354
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, Oct 22 2008
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EXTENSIONS
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More terms from Harvey P. Dale, Mar 05 2016
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STATUS
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approved
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