A092486 Take natural numbers, exchange first and third quadrisection.

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, 25, 28, 31, 30, 29, 32, 35, 34, 33, 36, 39, 38, 37, 40, 43, 42, 41, 44, 47, 46, 45, 48, 51, 50, 49, 52, 55, 54, 53, 56, 59, 58, 57, 60, 63, 62, 61, 64, 67, 66, 65, 68, 71, 70, 69, 72

Offset: 0

Author

Ralf Stephan, Apr 04 2004

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20003
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

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

Programs

Mathematica

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

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

Formula

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

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

a(n) = n+1+i^n+(-i)^n, where i is the imaginary unit. - Bruno Berselli, Feb 08 2011

From Wesley Ivan Hurt, May 09 2021: (Start)

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

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

Sum_{n>=0} (-1)^n/a(n) = log(2) (A002162). - Amiram Eldar, Nov 28 2023