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A092486 Take natural numbers, exchange first and third quadrisection. 6

%I #27 Nov 28 2023 10:57:04

%S 3,2,1,4,7,6,5,8,11,10,9,12,15,14,13,16,19,18,17,20,23,22,21,24,27,26,

%T 25,28,31,30,29,32,35,34,33,36,39,38,37,40,43,42,41,44,47,46,45,48,51,

%U 50,49,52,55,54,53,56,59,58,57,60,63,62,61,64,67,66,65,68,71,70,69,72

%N Take natural numbers, exchange first and third quadrisection.

%H Harry J. Smith, <a href="/A092486/b092486.txt">Table of n, a(n) for n = 0..20003</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.

%F G.f.: (3-4*x+3*x^2)/((1+x^2)*(1-x)^2).

%F a(4n) = 4n+3, a(4n+1) = 4n+2, a(4n+2) = 4n+1, a(4n+3) = 4n+4.

%F a(n) = n+1+i^n+(-i)^n, where i is the imaginary unit. - _Bruno Berselli_, Feb 08 2011

%F From _Wesley Ivan Hurt_, May 09 2021: (Start)

%F a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4).

%F a(n) = 1 + n + 2*cos(n*Pi/2). (End)

%F Sum_{n>=0} (-1)^n/a(n) = log(2) (A002162). - _Amiram Eldar_, Nov 28 2023

%t Flatten[Partition[Range[80],4]/.{a_,b_,c_,d_}->{c,b,a,d}] (* _Harvey P. Dale_, Aug 12 2012 *)

%o (PARI) { f="b092486.txt"; for (n=0, 5000, a0=4*n + 3; a1=a0 - 1; a2=a1 - 1; a3=a0 + 1; write(f, 4*n, " ", a0); write(f, 4*n+1, " ", a1); write(f, 4*n+2, " ", a2); write(f, 4*n+3, " ", a3); ); } \\ _Harry J. Smith_, Jun 21 2009]

%Y Cf. A002162, A080412, A064429, A074066, A080782, A159966.

%K nonn,easy

%O 0,1

%A _Ralf Stephan_, Apr 04 2004

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)