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A244884
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Expansion of (-2 +x^2 +x -x*sqrt(1-2*x-3*x^2))/(-1 +x -sqrt(1-2*x-3*x^2)).
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3
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1, 1, 1, 2, 5, 12, 30, 76, 196, 512, 1353, 3610, 9713, 26324, 71799, 196938, 542895, 1503312, 4179603, 11662902, 32652735, 91695540, 258215664, 728997192, 2062967382, 5850674704, 16626415975, 47337954326, 135015505407, 385719506620, 1103642686382
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OFFSET
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0,4
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COMMENTS
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For n > 1, a(n) is the number of Motzkin n-paths that start with an up step. - Gennady Eremin, Sep 18 2021
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LINKS
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FORMULA
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Conjecture D-finite with recurrence: (n+2)*a(n) +(-3*n-1)*a(n-1) -n*a(n-2) +3*(n-3)*a(n-3)=0. - R. J. Mathar, Jan 24 2020
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MATHEMATICA
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CoefficientList[Series[(-2 + x^2 + x - x Sqrt[1 - 2 x - 3 x^2])/(-1 + x - Sqrt[1 - 2 x - 3 x^2]), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 10 2014 *)
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PROG
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(PARI) my(x='x + O('x^50)); Vec((-2 +x^2 +x -x*sqrt(1-2*x-3*x^2))/(-1 +x -sqrt(1-2*x-3*x^2))) \\ G. C. Greubel, Feb 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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