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A304580 Period 16: repeat 1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6. 2

%I #21 Nov 19 2023 21:16:25

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

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

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

%N Period 16: repeat 1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6.

%C Repeating sequences of alternating odd and even single digits that in pairs sum to 9, 11 or 7. Note that 1836547290725436 = 20202020197979796 / 11.

%H Colin Barker, <a href="/A304580/b304580.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 (0,1,0,0,0,0,0,-1,0,1).

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

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

%F a(n) = a(n-2) - a(n-8) + a(n-10) for n > 10.

%F (End)

%t LinearRecurrence[{0,1,0,0,0,0,0,-1,0,1},{1,8,3,6,5,4,7,2,9,0},100] (* or *) PadRight[{},100,{1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6}] (* _Harvey P. Dale_, Sep 28 2021 *)

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

%Y Cf. A172423, A172430, A304583.

%K nonn,easy

%O 1,2

%A _Halfdan Skjerning_, May 15 2018

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)