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A290989
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Expansion of x^6*(1 + x^3)/(1 - 4*x + 5*x^2 - x^3 - 2*x^4 + x^6 + x^7 - 2*x^8 + x^9).
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3
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1, 4, 11, 26, 55, 109, 208, 389, 722, 1339, 2488, 4634, 8646, 16146, 30160, 56333, 105198, 196413, 366672, 684475, 1277701, 2385080, 4452277, 8311254, 15515091, 28963012, 54067156, 100930660, 188413624, 351723304, 656583197
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OFFSET
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6,2
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COMMENTS
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This corresponds to S(213,1,x) of Langley if one uses Theorem 8. Note that all three expressions for S(213;t,x), S(213;1,x) and the series on page 22 are mutually incompatible, so we show the sequence one would most likely see in other publications.
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LINKS
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FORMULA
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G.f.: x^6*(1 + x)*(1 - x + x^2)/((1 - x)*(1 - 2*x + x^3 - x^4)*(1 - x + x^4)).
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MATHEMATICA
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DeleteCases[#, 0] &@ CoefficientList[Series[x^6*(1+x^3)/(1 -4x +5x^2 -x^3 -2x^4 +x^6 +x^7 -2x^8 +x^9), {x, 0, 36}], x] (* Michael De Vlieger, Aug 16 2017 *)
LinearRecurrence[{4, -5, 1, 2, 0, -1, -1, 2, -1}, {1, 4, 11, 26, 55, 109, 208, 389, 722}, 80] (* Vincenzo Librandi, Aug 17 2017 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^6*(1+x^3)/((1-x)*(1-2*x+x^3-x^4)*(1-x+x^4)) )); // G. C. Greubel, Apr 12 2023
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^6*(1+x^3)/((1-x)*(1-x+x^4)*(1-2*x+x^3-x^4)) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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