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A176355
Periodic sequence: Repeat 6, 1.
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.
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)
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
KEYWORD
cofr,cons,easy,nonn,mult
AUTHOR
Klaus Brockhaus, Apr 15 2010
STATUS
approved