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%I #24 Mar 04 2024 01:09:30
%S 9,3,1,3,3,1,3,9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3,1,3,
%T 9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3,
%U 1,3,9,1,9,3,1,3,3,1,3,9,1,9,3,1,3,3
%N Period 9: repeat [9, 3, 1, 3, 3, 1, 3, 9, 1].
%C Greatest common divisor of (n+1)^2-1 and (n+1)^2+8. - _Bruno Berselli_, Mar 08 2017
%H Colin Barker, <a href="/A154629/b154629.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F a(n) = A147674(n)/9.
%F a(n) = A005563(n) / A144454(n+1) for n>0.
%F From _Colin Barker_, Dec 21 2017: (Start)
%F G.f.: (9 + 3*x + x^2 + 3*x^3 + 3*x^4 + x^5 + 3*x^6 + 9*x^7 + x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)).
%F a(n) = a(n-9) for n>8.
%F (End)
%t With[{n=5}, PadLeft[{}, 9n, {9,3,1,3,3,1,3,9,1}]] (* _Harvey P. Dale_, Oct 22 2011 *)
%o (PARI) Vec((9 + 3*x + x^2 + 3*x^3 + 3*x^4 + x^5 + 3*x^6 + 9*x^7 + x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^100)) \\ _Colin Barker_, Dec 21 2017
%Y Cf. A005563, A144454, A147674.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Jan 13 2009
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