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A064429 a(n) = floor(n / 3) * 3 + sign(n mod 3) * (3 - n mod 3). 9
0, 2, 1, 3, 5, 4, 6, 8, 7, 9, 11, 10, 12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22, 24, 26, 25, 27, 29, 28, 30, 32, 31, 33, 35, 34, 36, 38, 37, 39, 41, 40, 42, 44, 43, 45, 47, 46, 48, 50, 49, 51, 53, 52, 54, 56, 55, 57, 59, 58, 60, 62, 61, 63, 65, 64, 66, 68, 67, 69, 71, 70 (list; graph; refs; listen; history; text; internal format)
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)

The sequence is A008585 interleaved with A016789 and A016777.

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)

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..3000

Eric Weisstein's World of Mathematics, Alternating Permutations

Index entries for sequences that are permutations of the natural numbers

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) = A001477(n) + A102283(n). - 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)*(x-1)^2 ). - R. J. Mathar, Feb 20 2011

a(n) = 2n - 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

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

A064429:=n->2*n-3-3*floor((n-2)/3): seq(A064429(n), n=0..100); # Wesley Ivan Hurt, Nov 30 2013

MATHEMATICA

Table[2 n - 3 - 3 Floor[(n - 2)/3], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 30 2013 *)

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

Cf. A001477, A004442, A074066, A080425, A080782, A102283, A143097.

Sequence in context: A288538 A256210 A256371 * A234751 A113790 A181094

Adjacent sequences:  A064426 A064427 A064428 * A064430 A064431 A064432

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Oct 15 2001

STATUS

approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)