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A165207 Period 4: repeat [2, 2, 4, 4].

%I A165207 #32 Dec 12 2023 07:46:22
%S A165207 2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,
%T A165207 4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,
%U A165207 2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2,2,4,4,2
%N A165207 Period 4: repeat [2, 2, 4, 4].
%C A165207 Continued fraction expansion of (21+5*sqrt(26))/19 = A177153. - _Klaus Brockhaus_, May 03 2010
%C A165207 A045572(n)^a(n) == 1 (mod 10). For n>1, a(n) is the smallest positive exponent with this property. - _Christina Steffan_, Sep 08 2015
%H A165207 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).
%F A165207 a(n) = 2*A130658(n).
%F A165207 a(n) = A002378(n+1)/A064038(n+2) = A061037(4n+6)/A064038(n+2) = A061037(4n+6)/A061041(8n+12).
%F A165207 From _R. J. Mathar_, Sep 11 2009: (Start)
%F A165207 a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.
%F A165207 G.f.: 2*(1+2*x^2)/((1-x)*(1+x^2)). (End)
%F A165207 a(n) = 3-cos(Pi*n/2)-sin(Pi*n/2). - _R. J. Mathar_, Oct 08 2011
%F A165207 a(n) = 2 + (2*floor(n/2) mod 4). - _Wesley Ivan Hurt_, Apr 20 2015
%F A165207 a(n) = a(n-4) for n>3. - _Wesley Ivan Hurt_, Jul 09 2016
%p A165207 seq(op([2, 2, 4, 4]), n=0..50); # _Wesley Ivan Hurt_, Jul 09 2016
%t A165207 PadRight[{}, 120, {2,2,4,4}] (* _Harvey P. Dale_, Oct 08 2014 *)
%o A165207 (Magma) &cat[[2,2,4,4]^^30]; // _Vincenzo Librandi_, Feb 08 2016
%o A165207 (PARI) a(n)=n\2*2%4 + 2 \\ _Charles R Greathouse IV_, Jul 17 2016
%Y A165207 Cf. A002378, A045572, A061037, A061041, A064038, A130658, A177153.
%K A165207 nonn,easy
%O A165207 0,1
%A A165207 _Paul Curtz_, Sep 07 2009
%E A165207 Edited, offset set to 0, by _R. J. Mathar_, Sep 11 2009