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

0,1

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.

Links

Table of n, a(n) for n=0..104.

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

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

Example

0.6161616161616161616161616161616161616161...

Mathematica

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

Prog

(Magma) &cat[ [6, 1]: n in [0..52] ];
(Magma) [(7+5*(-1)^n)/2: n in [0..104]];

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).

Sequence in context: A349000 A344699 A010687 * A109918 A339433 A263494

Adjacent sequences: A176352 A176353 A176354 * A176356 A176357 A176358

Keyword

cofr,cons,easy,nonn,mult

Author

Klaus Brockhaus, Apr 15 2010

Status

approved