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A103889 Odd and even positive integers swapped. 26

%I

%S 2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19,22,21,24,23,26,25,

%T 28,27,30,29,32,31,34,33,36,35,38,37,40,39,42,41,44,43,46,45,48,47,50,

%U 49,52,51,54,53,56,55,58,57,60,59,62,61,64,63,66,65,68,67,70,69,72,71

%N Odd and even positive integers swapped.

%C (a(n)-1)*(a(n-1)+1) = 2*A176222(n+1) for n>1; (a(n)-1)*(a(n-3)+1) = 2*A176222(n) for n>3. - _Bruno Berselli_, Nov 16 2010

%C For n >= 5, also the number of (undirected) Hamiltonian cycles in the (n-2)-Moebius ladder. - _Eric W. Weisstein_, May 06 2019

%C For n >= 4, also the number of (undirected) Hamiltonian cycles in the (n-1)-prism graph. - _Eric W. Weisstein_, May 06 2019

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(2k) = 2k-1 = A005408(k), a(2k-1) = 2k = A005843(k), k=1, 2, ...

%F O.g.f.: x*(x^2-x+2)/[(x-1)^2*(1+x)]. - _R. J. Mathar_, Apr 06 2008

%F a(n) = n-1+2*(n mod 2). - _Rolf Pleisch_, Apr 22 2008

%F a(n) = 2*n-a(n-1)-1 (with a(1)=2). - _Vincenzo Librandi_, Nov 16 2010

%F a(n) = n-(-1)^n. a(n)-a(n-1)-a(n-2)+a(n-3) = 0 for n>3. - _Bruno Berselli_, Nov 16 2010

%t Table[{n + 1, n}, {n, 1, 100, 2}] // Flatten

%t Table[n - (-1)^n, {n, 25}] (* _Eric W. Weisstein_, May 06 2019 *)

%o [ n eq 1 select 2 else -Self(n-1)+2*n-1: n in [1..72] ];

%o (Haskell)

%o import Data.List (transpose)

%o a103889 n = n - 1 + 2 * mod n 2

%o a103889_list = concat $ transpose [tail a005843_list, a005408_list]

%o -- _Reinhard Zumkeller_, Jun 23 2013, Feb 21 2011

%o (PARI) a(n)=n-1+if(n%2,2) \\ _Charles R Greathouse IV_, Feb 24 2011

%Y Essentially the same as A014681.

%Y Odd numbers: A005408. Even numbers: A005843.

%Y Cf. A103889, A004442.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Feb 20 2005

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)