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A122595
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Expansion of x/(1 - 3*x + x^2 + x^3 - x^4).
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2
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1, 3, 8, 20, 50, 125, 313, 784, 1964, 4920, 12325, 30875, 77344, 193752, 485362, 1215865, 3045825, 7630000, 19113672, 47881056, 119945321, 300471235, 752701000, 1885567500, 4723475586, 11832629493, 29641546393, 74254101600
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OFFSET
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1,2
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REFERENCES
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Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
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LINKS
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FORMULA
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G.f.: x/(1 - 3*x + x^2 + x^3 - x^4).
a(n) = 3*a(n-1) - a(n-2) - a(n-3) + a(n-4) for n>4. - Wesley Ivan Hurt, Sep 18 2015
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EXAMPLE
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x + 3*x^2 + 8*x^3 + 20*x^4 + 50*x^5 + 125*x^6 + 313*x^7 + 784*x^8 + 1964*x^9 + ...
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MATHEMATICA
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nn = 30; CoefficientList[Series[x/(1 - 3*x + x^2 + x^3 - x^4), {x, 0, nn}], x]
LinearRecurrence[{3, -1, -1, 1}, {1, 3, 8, 20}, 40] (* Harvey P. Dale, Nov 09 2020 *)
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PROG
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(Magma) I:=[1, 3, 8, 20]; [n le 4 select I[n] else 3*Self(n-1)-Self(n-2)-Self(n-3)+Self(n-4): n in [1..40]] // Vincenzo Librandi, Aug 07 2012
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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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EXTENSIONS
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STATUS
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approved
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