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A193682
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Period 8: repeat [0, 1, 2, 3, 0, 3, 2, 1].
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6
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0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 3, 0
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OFFSET
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0,3
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COMMENTS
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This sequence can be continued periodically for negative values of n.
See a comment on A203571 where a k-family of 2k-periodic sequences P_k has been defined. The present sequence is P_4. - Wolfdieter Lang, Feb 02 2012
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LINKS
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FORMULA
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a(n) = n mod 4 if (-1)^floor(n/4)=+1, otherwise (4-n) mod 4, n >= 0. (-1)^floor(n/4) is the parity of the quotient floor(n/4). This quotient is sometimes denoted by n\4.
O.g.f.: x*(1+2*x+3*x^2+3*x^4+2*x^5+x^6)/( (1-x)*(1+x)*(1+x^2)*(1+x^4)).
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EXAMPLE
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a(10) = 10(mod 4) = 2 because 10\4 = floor(10/4)=2 is even; the parity is +1.
a(7) = (4-7)(mod 4) = 1 because 7\4 = floor(7/4)=1 is odd; the parity is -1.
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MATHEMATICA
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PadRight[{}, 120, {0, 1, 2, 3, 0, 3, 2, 1}] (* Vincenzo Librandi, Oct 17 2018 *)
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PROG
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(Python)
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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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