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%I #24 Oct 15 2017 19:01:39
%S 1,3,5,7,9,9,7,5,3,1,1,3,5,7,9,9,7,5,3,1,1,3,5,7,9,9,7,5,3,1,1,3,5,7,
%T 9,9,7,5,3,1,1,3,5,7,9,9,7,5,3,1,1,3,5,7,9,9,7,5,3,1,1
%N Period 10: repeat 1, 3, 5, 7, 9, 9, 7, 5, 3, 1.
%C For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 11 for the positive odd numbers not divisible by 11, which are given in A204454.
%C The underlying period length 22 sequence with offset 0 is P_11, also called Modd11, periodic([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,1).
%F a(n) = A204454(n) (Modd 11) := Modd11(A204454(n)), with the periodic sequence Modd11 with period length 22 given in the comment section.
%F O.g.f.: x*(1+x^9+3*x*(1+x^7)+5*x^2*(1+x^5)+7*x^3*(1+x^3)+9*x^4*(1+x))/(1-x^10) = x*(1+x)*(1-x^5)/((1+x^5)*(1-x)^2).
%e Residue Modd 11 of the positive odd numbers not divisible by 11:
%e A204454: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, ...
%e Modd 11: 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, ...
%t PadRight[{},120,{1,3,5,7,9,9,7,5,3,1}] (* or *) LinearRecurrence[{2,-2,2,-2,1},{1,3,5,7,9},120] (* _Harvey P. Dale_, Oct 15 2017 *)
%o (PARI) a(n)=[1, 3, 5, 7, 9, 9, 7, 5, 3, 1][n%10+1] \\ _Charles R Greathouse IV_, Jul 17 2016
%Y Cf. A000012 (Modd 3), A084101 (Modd 5), A110551 (Modd 7).
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 09 2012
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