A247555 A permutation of the nonnegative numbers: a(4n) = 8n, a(4n+1) = 2n + 1, a(4n+2) = 4n + 2, a(4n+3) = 8n + 4.

0, 1, 2, 4, 8, 3, 6, 12, 16, 5, 10, 20, 24, 7, 14, 28, 32, 9, 18, 36, 40, 11, 22, 44, 48, 13, 26, 52, 56, 15, 30, 60, 64, 17, 34, 68, 72, 19, 38, 76, 80, 21, 42, 84, 88, 23, 46, 92, 96, 25, 50, 100, 104, 27, 54, 108, 112, 29, 58, 116, 120

Offset: 0

Author

Paul Curtz, Sep 19 2014

Keywords

• nonn
• easy
• less

Comments

A permutation of the nonnegative integers.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Crossrefs

Cf. A005408, A008590, A016825, A017113, A225055, A001477, A111284.

Programs

Magma

&cat[[4*(i-1),i,2*i,4*i]: i in [1..50 by 2]]; // Bruno Berselli, Sep 19 2014

Mathematica

a[n_]:=Switch[Mod[n,4],0,2 n,1,(n+1)/2,2,n,3,2 n-2]; Table[a[n],{n,0,60}] (* Jean-François Alcover, Oct 09 2014 *)
LinearRecurrence[{0,0,0,2,0,0,0,-1}, {0,1,2,4,8,3,6,12}, 50] (* G. C. Greubel, May 01 2018 *)

PARI

Vec(x*(4*x^6+2*x^5+x^4+8*x^3+4*x^2+2*x+1)/((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100)) \\ Colin Barker, Sep 19 2014

Formula

a(n) = a(n-4) + a(n-8) - a(n-12).

a(n) = 2*a(n-4) - a(n-8). - Colin Barker, Sep 19 2014

G.f.: x*(4*x^6 + 2*x^5 + x^4 + 8*x^3 + 4*x^2 + 2*x + 1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Sep 19 2014

a(n) = (11*n-3+(n+3)*(-1)^n+(4*n-1+(-1)^n)*cos(n*Pi/2)+2*(9-3*n+4(-1)^n)* sin(n*Pi/2))/8. - Wesley Ivan Hurt, May 07 2021