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

Author

Klaus Brockhaus, Apr 07 2010

Keywords

• cofr
• cons
• nonn
• easy

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

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

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).

Programs

Haskell

a176059 = (3 -) . (`mod` 2) -- Reinhard Zumkeller, Nov 27 2012

Haskell

a176059_list = cycle [3,2]  -- Reinhard Zumkeller, Apr 04 2012

Magma

&cat[ [3, 2]: n in [0..52] ];
[ (5+(-1)^n)/2: n in [0..104] ];

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 *)

PARI

a(n)=3-n%2 \\ Charles R Greathouse IV, Jul 13 2016

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)).

E.g.f.: 3*cosh(x) + 2*sinh(x). - Stefano Spezia, Aug 04 2025