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A176355 Periodic sequence: Repeat 6, 1.

%I A176355 #27 Feb 09 2025 13:34:19
%S A176355 6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,
%T A176355 6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,
%U A176355 6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6
%N A176355 Periodic sequence: Repeat 6, 1.
%C A176355 Interleaving of A010722 and A000012.
%C A176355 Also continued fraction expansion of 3+sqrt(15).
%C A176355 Also decimal expansion of 61/99.
%C A176355 Essentially first differences of A047335.
%C A176355 Binomial transform of 6 followed by A166577 without initial terms 1, 4.
%C A176355 Inverse binomial transform of A005009 preceded by 6.
%H A176355 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A176355 G.f.: (6 + x)/(1 - x^2).
%F A176355 a(n) = (7 + 5*(-1)^n)/2.
%F A176355 a(n) = a(n-2) for n>1, a(0)=6, a(1)=1.
%F A176355 a(n) = -a(n-1)+7 for n>0, a(0)=6.
%F A176355 a(n) = 6*((n+1) mod 2) + (n mod 2).
%F A176355 a(n) = A010687(n+1).
%F A176355 a(n) = 13^n mod 7. - _Vincenzo Librandi_, Jun 01 2016
%F A176355 From _Amiram Eldar_, Jan 01 2023: (Start)
%F A176355 Multiplicative with a(2^e) = 6, and a(p^e) = 1 for p >= 3.
%F A176355 Dirichlet g.f.: zeta(s)*(1+5/2^s). (End)
%F A176355 E.g.f.: 6*cosh(x) + sinh(x). - _Stefano Spezia_, Feb 09 2025
%e A176355 0.6161616161616161616161616161616161616161...
%t A176355 PadRight[{},120,{6,1}] (* _Harvey P. Dale_, Apr 12 2018 *)
%o A176355 (Magma) &cat[ [6, 1]: n in [0..52] ];
%o A176355 (Magma) [(7+5*(-1)^n)/2: n in [0..104]];
%Y A176355 Cf. A010722 (all 6's sequence), A000012 (all 1's sequence), A092294 (decimal expansion of 3+sqrt(15)), A010687 (repeat 1, 6), A047335 (congruent to 0 or 6 mod 7), A166577, A005009 (7*2^n).
%K A176355 cofr,cons,easy,nonn,mult
%O A176355 0,1
%A A176355 _Klaus Brockhaus_, Apr 15 2010