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 A064429 a(n) = floor(n / 3) * 3 + sign(n mod 3) * (3 - n mod 3). 10
 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) 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) = 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)*(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) 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 *) {#+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 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 27 17:42 EST 2023. Contains 359845 sequences. (Running on oeis4.)