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%I #18 Jan 01 2023 02:28:59
%S 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 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 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 Periodic sequence: Repeat 5, 1.
%C Interleaving of A010716 and A000012.
%C Also continued fraction expansion of (5+3*sqrt(5))/2.
%C Also decimal expansion of 17/33.
%C Essentially first differences of A047264.
%C Binomial transform of 5 followed by -A122803 without initial terms 1, -2.
%C Inverse binomial transform of 5 followed by A007283 without initial term 3.
%C Second inverse binomial transform of A168607 without initial term 3.
%C 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(n) = 3+2*(-1)^n.
%F a(n) = a(n-2) for n > 1; a(0) = 5, a(1) = 1.
%F a(n) = -a(n-1)+6 for n > 0; a(0) = 5.
%F a(n) = 5*((n+1) mod 2)+(n mod 2).
%F a(n) = A010686(n+1).
%F G.f.: (5+x)/(1-x^2).
%F From _Amiram Eldar_, Jan 01 2023: (Start)
%F Multiplicative with a(2^e) = 5, and a(p^e) = 1 for p >= 3.
%F Dirichlet g.f.: zeta(s)*(1+2^(2-s)). (End)
%o (Magma) &cat[ [5, 1]: n in [0..52] ];
%o [ 3+2*(-1)^n: n in [0..104] ];
%Y 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 cofr,cons,easy,nonn,mult
%O 0,1
%A _Klaus Brockhaus_, Apr 13 2010
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