A176059 Periodic sequence: Repeat 3, 2.

3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3

Offset

0,1

Comments

Interleaving of A010701 and A007395.

Also continued fraction expansion of (3+sqrt(15))/2.

Also decimal expansion of 32/99.

a(n) = A010693(n+1).

Essentially first differences of A047218.

Binomial transform of 3 followed by -A122803.

Inverse binomial transform of 3 followed by A020714.

Second inverse binomial transform of A057198 without initial term 1.

Links

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

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

Formula

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

a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = 2.

a(n) = -a(n-1)+5 for n > 0; a(0) = 3.

a(n) = 3*((n+1) mod 2)+2*(n mod 2).

G.f.: (3+2*x)/((1-x)*(1+x)).

Maple

A176059:=n->(5+(-1)^n)/2; seq(A176059(n), n=0..100); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

a[n_] := {3, 2}[[Mod[n, 2] + 1]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Jul 19 2013 *)
PadRight[{}, 120, {3, 2}] (* Harvey P. Dale, Oct 06 2019 *)

Prog

(Magma) &cat[ [3, 2]: n in [0..52] ];
[ (5+(-1)^n)/2: n in [0..104] ];
(Haskell)
a176059 = (3 -) . (`mod` 2) -- Reinhard Zumkeller, Nov 27 2012
(Haskell)
a176059_list = cycle [3, 2]  -- Reinhard Zumkeller, Apr 04 2012
(PARI) a(n)=3-n%2 \\ Charles R Greathouse IV, Jul 13 2016

Crossrefs

Cf. A010701 (all 3's sequence), A007395 (all 2's sequence), A176058 (decimal expansion of (3+sqrt(15))/2), A010693 (repeat 2, 3), A047218 (congruent to {0, 3} mod 5), A122803 (powers of -2), A020714 (5*2^n), A057198 ((5*3^(n-1)+1)/2, n > 0).

Cf. A026532 (partial products).

Sequence in context: A308006 A049071 A168330 * A262785 A264843 A316290

Adjacent sequences: A176056 A176057 A176058 * A176060 A176061 A176062

Keyword

cofr,cons,nonn,easy

Author

Klaus Brockhaus, Apr 07 2010

Status

approved