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

0,1

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.

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

Mathematica

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

Prog

(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]

Crossrefs

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

Sequence in context: A208153 A348013 A105033 * A159966 A119263 A028412

Adjacent sequences: A092483 A092484 A092485 * A092487 A092488 A092489

Keyword

nonn,easy

Author

Ralf Stephan, Apr 04 2004

Status

approved