A216972 a(4n+2) = 2, otherwise a(n) = n.

0, 1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 12, 13, 2, 15, 16, 17, 2, 19, 20, 21, 2, 23, 24, 25, 2, 27, 28, 29, 2, 31, 32, 33, 2, 35, 36, 37, 2, 39, 40, 41, 2, 43, 44, 45, 2, 47, 48, 49, 2, 51, 52, 53, 2, 55, 56, 57, 2, 59, 60, 61, 2, 63, 64, 65, 2, 67, 68, 69, 2

Offset: 0

Author

Paul Curtz, Sep 21 2012

Keywords

• nonn
• easy

Comments

For n>0, a(n) is the denominator of A214282(n)/(-A214283(n+1)):

1/1, 1/2, 1/3, 3/4, 3/5, 1/2, 3/7, 5/8, 5/9, ...

For n>0, a(n) is the denominator of A214283(n)/A214283(n+1):

0/1, 1/2, 2/3, 3/4, 2/5, 1/2, 4/7, 5/8, 4/9, ...

a(n), first and second differences:

0, 1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 12, ...

1, 1, 1, 1, 1, -3, 5, 1, 1, -7, 9, 1, 1, ...

0, 0, 0, 0, -4, 8, -4, 0, -8, 16, -8, 0, -12, ...

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Crossrefs

Cf. A028233, A034684, A000265, A026741, A060819, A145979, A214682.

Programs

Magma

[n mod 4 eq 2 select 2 else n: n in [0..70]]; // Bruno Berselli, Sep 26 2012

Mathematica

a[n_] := If[Mod[n, 4] == 2, 2, n]; Table[a[n], {n, 0, 81}] (* Jean-François Alcover, Sep 25 2012 *)
LinearRecurrence[{0,0,0,2,0,0,0,-1},{0,1,2,3,4,5,2,7},80] (* Harvey P. Dale, Nov 06 2017 *)

Maxima

makelist(expand(2+(4-(1+(-1)^n)*(1-%i^n))*(n-2)/4), n, 0, 70); /* Bruno Berselli, Sep 26 2012 */

Python

def A216972(n): return 2 if n&3==2 else n # Chai Wah Wu, Jan 31 2024

Formula

a(n) = 2*a(n-4) - a(n-8).

a(n+4) - a(n) = 4*A152822(n).

a(2n) + a(2n+1) = |A141124(n)|.

a(4n) + a(4n+1) + a(4n+2) + a(4n+3) = 6*A005408(n) = A017593(n).

G.f.: (x+2*x^2+3*x^3+4*x^4+3*x^5-2*x^6+x^7) / (1-2*x^4+x^8). - Jean-François Alcover, Sep 25 2012

a(n) = 2+(4-(1+(-1)^n)*(1-i^n))*(n-2)/4, where i=sqrt(-1). - Bruno Berselli, Sep 26 2012

a(2n) = 2*|A009531(n)|, a(2n+1) = 2n+1. - Bruno Berselli, Sep 27 2012