OFFSET
0,3
COMMENTS
1/1, 1/2, 1/3, 3/4, 3/5, 1/2, 3/7, 5/8, 5/9, ...
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).
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)|.
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
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 *)
PROG
(Magma) [n mod 4 eq 2 select 2 else n: n in [0..70]]; // Bruno Berselli, Sep 26 2012
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 21 2012
STATUS
approved