A174927 Periodic sequence: Repeat 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, 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, 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

Offset: 0

Author

Klaus Brockhaus, Apr 02 2010

Keywords

• cofr
• easy
• nonn

Comments

Interleaving of A000012 and 2*A010871.

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

First differences of A174928.

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 1).

Crossrefs

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

Programs

Magma

&cat[ [1, 64]: n in [0..41] ];
[ (65-63*(-1)^n)/2: n in [0..83] ];

Mathematica

PadRight[{},100,{1,64}] (* Harvey P. Dale, Jun 16 2013 *)

Formula

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

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

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

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

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