A176355 Periodic sequence: Repeat 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, 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, 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

Offset: 0

Author

Klaus Brockhaus, Apr 15 2010

Keywords

• cofr
• cons
• easy
• nonn
• mult

Comments

Interleaving of A010722 and A000012.

Also continued fraction expansion of 3+sqrt(15).

Also decimal expansion of 61/99.

Essentially first differences of A047335.

Binomial transform of 6 followed by A166577 without initial terms 1, 4.

Inverse binomial transform of A005009 preceded by 6.

Examples

			0.6161616161616161616161616161616161616161...
		

Links

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

Crossrefs

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).

Programs

Magma

&cat[ [6, 1]: n in [0..52] ];

Magma

[(7+5*(-1)^n)/2: n in [0..104]];

Mathematica

PadRight[{},120,{6,1}] (* Harvey P. Dale, Apr 12 2018 *)

Formula

G.f.: (6 + x)/(1 - x^2).

a(n) = (7 + 5*(-1)^n)/2.

a(n) = a(n-2) for n>1, a(0)=6, a(1)=1.

a(n) = -a(n-1)+7 for n>0, a(0)=6.

a(n) = 6*((n+1) mod 2) + (n mod 2).

a(n) = A010687(n+1).

a(n) = 13^n mod 7. - Vincenzo Librandi, Jun 01 2016

From Amiram Eldar, Jan 01 2023: (Start)

Multiplicative with a(2^e) = 6, and a(p^e) = 1 for p >= 3.

Dirichlet g.f.: zeta(s)*(1+5/2^s). (End)

E.g.f.: 6*cosh(x) + sinh(x). - Stefano Spezia, Feb 09 2025