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

%I A216972 #51 Feb 16 2024 12:32:18
%S A216972 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,
%T A216972 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,
%U A216972 53,2,55,56,57,2,59,60,61,2,63,64,65,2,67,68,69,2
%N A216972 a(4n+2) = 2, otherwise a(n) = n.
%C A216972 For n>0, a(n) is the denominator of A214282(n)/(-A214283(n+1)):
%C A216972 1/1, 1/2, 1/3, 3/4, 3/5, 1/2, 3/7, 5/8, 5/9, ...
%C A216972 For n>0, a(n) is the denominator of A214283(n)/A214283(n+1):
%C A216972 0/1, 1/2, 2/3, 3/4, 2/5, 1/2, 4/7, 5/8, 4/9, ...
%C A216972 a(n), first and second differences:
%C A216972 0, 1, 2, 3,  4,  5,  2, 7,  8,  9,  2, 11,  12, ...
%C A216972 1, 1, 1, 1,  1, -3,  5, 1,  1, -7,  9,  1,   1, ...
%C A216972 0, 0, 0, 0, -4,  8, -4, 0, -8, 16, -8,  0, -12, ...
%H A216972 Bruno Berselli, <a href="/A216972/b216972.txt">Table of n, a(n) for n = 0..1000</a>
%H A216972 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A216972 a(n) = 2*a(n-4) - a(n-8).
%F A216972 a(n+4) - a(n) = 4*A152822(n).
%F A216972 a(2n) + a(2n+1) = |A141124(n)|.
%F A216972 a(4n) + a(4n+1) + a(4n+2) + a(4n+3) = 6*A005408(n) = A017593(n).
%F A216972 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
%F A216972 a(n) = 2+(4-(1+(-1)^n)*(1-i^n))*(n-2)/4, where i=sqrt(-1). - _Bruno Berselli_, Sep 26 2012
%F A216972 a(2n) = 2*|A009531(n)|, a(2n+1) = 2n+1. - _Bruno Berselli_, Sep 27 2012
%t A216972 a[n_] := If[Mod[n, 4] == 2, 2, n]; Table[a[n], {n, 0, 81}] (* _Jean-François Alcover_, Sep 25 2012 *)
%t A216972 LinearRecurrence[{0,0,0,2,0,0,0,-1},{0,1,2,3,4,5,2,7},80] (* _Harvey P. Dale_, Nov 06 2017 *)
%o A216972 (Magma) [n mod 4 eq 2 select 2 else n: n in [0..70]]; // _Bruno Berselli_, Sep 26 2012
%o A216972 (Maxima) makelist(expand(2+(4-(1+(-1)^n)*(1-%i^n))*(n-2)/4), n, 0, 70); /* _Bruno Berselli_, Sep 26 2012 */
%o A216972 (Python)
%o A216972 def A216972(n): return 2 if n&3==2 else n # _Chai Wah Wu_, Jan 31 2024
%Y A216972 Cf. A028233, A034684, A000265, A026741, A060819, A145979, A214682.
%K A216972 nonn,easy
%O A216972 0,3
%A A216972 _Paul Curtz_, Sep 21 2012