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A080456
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a(1) = a(2) = 2; for n > 2, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
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6
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2, 2, 6, 10, 14, 18, 18, 22, 26, 30, 30, 34, 38, 42, 42, 46, 50, 54, 54, 58, 62, 66, 66, 70, 74, 78, 78, 82, 86, 90, 90, 94, 98, 102, 102, 106, 110, 114, 114, 118, 122, 126, 126, 130, 134, 138, 138, 142, 146, 150, 150, 154, 158, 162, 162, 166, 170, 174, 174
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OFFSET
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1,1
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COMMENTS
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First differences are 4-periodic.
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LINKS
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Table of n, a(n) for n=1..59.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
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FORMULA
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a(n) = -2 + 4*((n+2) mod (n+1)) + Sum_{k=0..n} ((1/2)*((k mod 4) + ((k+1) mod 4) - ((k+2) mod 4) + 3*((k+3) mod 4))). - Paolo P. Lava, Aug 29 2007
From Chai Wah Wu, Jul 17 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 6.
G.f.: -2*(-1 - 2*x^2 - 2*x^3 - x^4 - 2*x^5 + 2*x^6)/((-1 + x)^2*(1 + x + x^2 + x^3)). (End)
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MATHEMATICA
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Join[{2}, LinearRecurrence[{1, 0, 0, 1, -1}, {6, 10, 14, 18, 18}, 60]] (* Jean-François Alcover, Sep 02 2018 *)
CoefficientList[Series[-2*(-1 - 2 x^2 - 2 x^3 - x^4 - 2 x^5 + 2 x^6)/((-1 + x)^2 (1 + x +x^2 + x^3)), {x, 0, 60}], x] (* Stefano Spezia, Sep 02 2018 *)
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CROSSREFS
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Cf. A080455, A080457, A080458, A080036, A080037.
Sequence in context: A081728 A197218 A080460 * A077017 A181551 A127404
Adjacent sequences: A080453 A080454 A080455 * A080457 A080458 A080459
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Mar 20 2003
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EXTENSIONS
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a(1) = 2 prepended by Stefano Spezia, Sep 04 2018
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STATUS
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approved
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