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Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.
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%I #28 Feb 10 2024 17:31:32

%S 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8,1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,

%T 3,8,1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8,1,8,3,6,5,4,7,2,9,0,9,2,7,4,

%U 5,6,3,8,1,8,3,6,5,4,7,2,9,0,9,2,7,4

%N Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.

%C Repeating sequences of alternating odd and even single digits that in pairs sum to 9 or 11. Note that 183654729092745638 = 2020202020020202018 / 11.

%H Colin Barker, <a href="/A304583/b304583.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,0,0,0,0,0,0,1,1).

%F From _Colin Barker_, May 28 2018: (Start)

%F G.f.: x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)).

%F a(n) = -a(n-1) + a(n-9) + a(n-10) for n > 10.

%F (End)

%t PadRight[{},120,{1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8}] (* _Harvey P. Dale_, Feb 10 2024 *)

%o (PARI) Vec(x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^50)) \\ _Colin Barker_, May 28 2018

%Y Cf. A172423, A172430, A304580.

%K nonn,easy

%O 1,2

%A _Halfdan Skjerning_, May 15 2018