OFFSET
0,2
COMMENTS
a(a(n)) = n (a self-inverse permutation).
Take natural numbers, exchange trisections starting with 1 and 2.
Lodumo_3 of A080425. - Philippe Deléham, Apr 26 2009
From Franck Maminirina Ramaharo, Jul 27 2018: (Start)
a(n) is also obtained as follows: write n in base 3; if the rightmost digit is '1', then replace it with '2' and vice versa; convert back to decimal. For example a(14) = a('11'2') = '11'1' = 13 and a(10) = a('10'1') = '10'2' = 11. (End)
A permutation of the nonnegative integers partitioned into triples [3*k-3, 3*k-1, 3*k-2] for k > 0. - Guenther Schrack, Feb 05 2020
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..3000
Eric Weisstein's World of Mathematics, Alternating Permutations.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
a(n) = A080782(n+1) - 1.
a(n) = n - 2*sin(4*Pi*n/3)/sqrt(3). - Jaume Oliver Lafont, Dec 05 2008
a(n) = lod_3(A080425(n)). - Philippe Deléham, Apr 26 2009
G.f.: x*(2 - x + 2*x^2)/((1 + x + x^2)*(1 - x)^2 ). - R. J. Mathar, Feb 20 2011
a(n) = 2*n - 3 - 3*floor((n-2)/3). - Wesley Ivan Hurt, Nov 30 2013
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3. - Wesley Ivan Hurt, Oct 06 2017
E.g.f.: x*exp(x) + (2*sin((sqrt(3)*x)/2))/(exp(x/2)*sqrt(3)). - Franck Maminirina Ramaharo, Jul 27 2018
From Guenther Schrack, Feb 05 2020: (Start)
a(n) = a(n-3) + 3 with a(0)=0, a(1)=2, a(2)=1 for n > 2;
a(n) = n + (w^(2*n) - w^n)*(1 + 2*w)/3 where w = (-1 + sqrt(-3))/2. (End)
Sum_{n>=1} (-1)^n/a(n) = log(2)/3. - Amiram Eldar, Jan 31 2023
EXAMPLE
From Franck Maminirina Ramaharo, Jul 27 2018: (Start)
Interleave 3 sequences:
A008585: 0.....3.....6.....9.......12.......15........
A016789: ..2.....5.....8.....11.......14.......17.....
A016777: ....1.....4.....7......10.......13.......16..
(End)
MAPLE
MATHEMATICA
Table[2 n - 3 - 3 Floor[(n - 2)/3], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 30 2013 *)
{#+1, #-1, #}[[Mod[#, 3, 1]]]&/@Range[0, 100] (* Federico Provvedi, May 11 2021 *)
PROG
(PARI) a(n) = 2*n-3-3*((n-2)\3); \\ Altug Alkan, Oct 06 2017
(GAP) a:=[0, 2, 1, 3];; for n in [5..100] do a[n]:=a[n-1]+a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Jul 27 2018
(Magma) [2*n - 3 - 3*((n-2) div 3): n in [0..80]]; // Vincenzo Librandi, Aug 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 15 2001
STATUS
approved