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A043547
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Odd numbers interspersed with double the previous odd number.
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10
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1, 2, 3, 6, 5, 10, 7, 14, 9, 18, 11, 22, 13, 26, 15, 30, 17, 34, 19, 38, 21, 42, 23, 46, 25, 50, 27, 54, 29, 58, 31, 62, 33, 66, 35, 70, 37, 74, 39, 78, 41, 82, 43, 86, 45, 90, 47, 94, 49, 98, 51, 102, 53, 106, 55, 110, 57, 114, 59, 118, 61, 122, 63, 126, 65, 130, 67, 134
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OFFSET
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1,2
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COMMENTS
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As pointed out by E. Angelini on the SeqFan list (cf. link), this is the lexicographically earliest sequence of positive integers without repetitions such that the sum of four consecutive terms is always a multiple of 4. - M. F. Hasler, Mar 22 2013
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LINKS
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FORMULA
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a(n) = (2 - n) * (n - floor(n/2) * 2) + 2 * (n - 1).
G.f.: x*(1+2*x)*(1+x^2)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003
a(n) = 2*a(n-2) - a(n-4) for n>4.
a(n) = n*(-1)^n/2 - (-1)^n + 3*n/2 - 1. (End)
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EXAMPLE
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a(1)=1 because n is odd. a(2)=2 because a(1)*2=2.
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MAPLE
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MATHEMATICA
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Flatten[Table[Accumulate[{2 n - 1, 2 n - 1}], {n, 40}]] (* Wesley Ivan Hurt, Nov 22 2015 *)
With[{o=Range[1, 71, 2]}, Riffle[o, 2o]] (* Harvey P. Dale, Sep 17 2019 *)
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PROG
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(Magma) [n*(-1)^n/2-(-1)^n+3*n/2-1 : n in [1..50]]; // Wesley Ivan Hurt, Nov 22 2015
(PARI) Vec(x*(1+2*x)*(1+x^2)/(1-x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 22 2015
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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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Jim Cook (jcook(AT)halcyon.com), Mar 01 2000
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EXTENSIONS
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STATUS
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approved
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