A174927 - OEIS

%I #7 Jun 30 2023 15:15:29

%S 1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,

%T 64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,

%U 1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,64

%N Periodic sequence: Repeat 1, 64.

%C Interleaving of A000012 and 2*A010871.

%C Also continued fraction expansion of (4+sqrt(17))/8.

%C First differences of A174928.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1).

%F a(n) = (65-63*(-1)^n)/2.

%F a(n) = a(n-2) for n > 1; a(0) = 0, a(1) = 64.

%F a(n) = -a(n-1)+65 for n > 0; a(0) = 1.

%F a(n) = ((n+1) mod 2)+64*(n mod 2).

%F G.f.: (1+64*x)/((1-x)*(1+x)).

%t PadRight[{},100,{1,64}] (* _Harvey P. Dale_, Jun 16 2013 *)

%o (Magma) &cat[ [1, 64]: n in [0..41] ];

%o [ (65-63*(-1)^n)/2: n in [0..83] ];

%Y Cf. A000012 (all 1's sequence), A010871 (all 32's sequence), A010689 (repeat 1, 8), A174930 (decimal expansion of (4+sqrt(17))/8), A174928.

%K cofr,easy,nonn

%O 0,2

%A _Klaus Brockhaus_, Apr 02 2010