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A116551
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Permutation of natural numbers generated by 3-rowed array shown below.
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1
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0, 3, 1, 6, 4, 2, 9, 7, 5, 12, 10, 8, 15, 13, 11, 18, 16, 14, 21, 19, 17, 24, 22, 20, 27, 25, 23, 30, 28, 26, 33, 31, 29, 36, 34, 32, 39, 37, 35, 42, 40, 38, 45, 43, 41, 48, 46, 44, 51, 49, 47, 54, 52, 50, 57, 55, 53, 60, 58, 56, 63, 61, 59, 66, 64, 62, 69, 67, 65, 72, 70, 68, 75
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OFFSET
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1,2
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COMMENTS
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0 3 6 9 12 15 18 21 24 ... a(n)= 3n
1 4 7 10 13 16 19 22 25 ... a(n)= 3n+1
2 5 8 11 14 17 20 23 26 ... a(n)= 3n+2
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REFERENCES
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M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997.
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LINKS
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FORMULA
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Starting at the term a(3), a(n+3k) = a(n) + 3k, with k>=1.
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 7.
G.f.: x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1). (End)
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MATHEMATICA
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Rest[CoefficientList[Series[x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1), {x, 0, 50}], x]] (* or *) Join[{0, 3, 1, 6, 4, 2, 9}, LinearRecurrence[{1, 0, 1, -1}, {7, 5, 12, 10}, 50]] (* G. C. Greubel, Sep 20 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1)) \\ G. C. Greubel, Sep 20 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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