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A246943
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a(4n) = 4*n , a(2n+1) = 8*n+4 , a(4n+2) = 2*n+1.
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2
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0, 4, 1, 12, 4, 20, 3, 28, 8, 36, 5, 44, 12, 52, 7, 60, 16, 68, 9, 76, 20, 84, 11, 92, 24, 100, 13, 108, 28, 116, 15, 124, 32, 132, 17, 140, 36, 148, 19, 156, 40, 164, 21, 172, 44, 180, 23, 188, 48, 196, 25, 204, 52, 212, 27, 220, 56, 228
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OFFSET
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0,2
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COMMENTS
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Consider the denominators of the Balmer series A061038(n) = 0, 4, 1, 36, 16, 100,... (a permutation of the squares of the nonnegative numbers i.e. A000290(n)) divided by A028310(n)=1,1,2,... . The numerators are a(n). The denominators are A138191(n).
a(3n) is divisible by the period 3 sequence: repeat 9, 3, 3.
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LINKS
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FORMULA
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G.f.: x*(4*x^6+x^5+12*x^4+4*x^3+12*x^2+x+4) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Sep 08 2014
a(n) = n*(19-13*(-1)^n+(1+(-1)^n)*(-1)^((2*n-1+(-1)^n)/4))/8. - Luce ETIENNE, May 26 2015
a(n) = n*(19-(-1)^n*13+2*cos(n*Pi/2))/8. - Giovanni Resta, May 26 2015
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EXAMPLE
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Numerators of a(0)=0/1=0, a(1)=4/1=4, a(2)=1/2, a(3)=36/3=12,... .
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MAPLE
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {0, 4, 1, 12, 4, 20, 3, 28}, 60] (* Harvey P. Dale, Jun 22 2022 *)
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PROG
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(PARI) concat(0, Vec(x*(4*x^6+x^5+12*x^4+4*x^3+12*x^2+x+4)/((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100))) \\ Colin Barker, Sep 08 2014
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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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