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A176260 Periodic sequence: Repeat 5, 1.

%I A176260 #22 Feb 09 2025 18:09:36
%S A176260 5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,
%T A176260 5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,
%U A176260 5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5
%N A176260 Periodic sequence: Repeat 5, 1.
%C A176260 Interleaving of A010716 and A000012.
%C A176260 Also continued fraction expansion of (5+3*sqrt(5))/2.
%C A176260 Also decimal expansion of 17/33.
%C A176260 Essentially first differences of A047264.
%C A176260 Binomial transform of 5 followed by -A122803 without initial terms 1, -2.
%C A176260 Inverse binomial transform of 5 followed by A007283 without initial term 3.
%C A176260 Second inverse binomial transform of A168607 without initial term 3.
%C A176260 Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 3*x^2 + 3*x^3 + 6*x^4 + 6*x^5 + ... is the o.g.f. for A008805. - _Peter Bala_, Mar 13 2015
%H A176260 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A176260 a(n) = 3+2*(-1)^n.
%F A176260 a(n) = a(n-2) for n > 1; a(0) = 5, a(1) = 1.
%F A176260 a(n) = -a(n-1)+6 for n > 0; a(0) = 5.
%F A176260 a(n) = 5*((n+1) mod 2)+(n mod 2).
%F A176260 a(n) = A010686(n+1).
%F A176260 G.f.: (5+x)/(1-x^2).
%F A176260 From _Amiram Eldar_, Jan 01 2023: (Start)
%F A176260 Multiplicative with a(2^e) = 5, and a(p^e) = 1 for p >= 3.
%F A176260 Dirichlet g.f.: zeta(s)*(1+2^(2-s)). (End)
%F A176260 E.g.f.: 5*cosh(x) + sinh(x). - _Stefano Spezia_, Feb 09 2025
%o A176260 (Magma) &cat[ [5, 1]: n in [0..52] ];
%o A176260 [ 3+2*(-1)^n: n in [0..104] ];
%Y A176260 Cf. A010716 (all 5's sequence), A000012 (all 1's sequence), A090550 (decimal expansion of (5+3*sqrt(5))/2), A010686 (repeat 1, 5), A047264 (congruent to 0 or 5 mod 6), A122803 (powers of -2), A007283 (3*2^n), A168607 (3^n+2), A008805.
%K A176260 cofr,cons,easy,nonn,mult
%O A176260 0,1
%A A176260 _Klaus Brockhaus_, Apr 13 2010