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A087777 a(1) = ... = a(4) = 1; a(n) = a(n - a(n-2)) + a(n - a(n-4)).

%I A087777 #45 Sep 08 2022 08:45:11
%S A087777 1,1,1,1,2,4,6,7,7,5,3,8,9,11,12,9,9,13,11,9,13,16,13,19,16,11,14,16,
%T A087777 21,22,14,14,19,17,22,27,25,16,20,28,22,22,26,25,24,32,26,22,29,29,32,
%U A087777 35,32,27,26,34,30,33,40,25,27,46,40,33,32,28,36,50,44,31,36,38,46,53,41,29,41
%N A087777 a(1) = ... = a(4) = 1; a(n) = a(n - a(n-2)) + a(n - a(n-4)).
%C A087777 This is the sequence Q(2,4) in the Hofstadter-Huber classification.
%C A087777 It is not known if this sequence is defined for all positive n. Balamohan et al. comment that it shows "inscrutably wild behavior".
%H A087777 N. J. A. Sloane, <a href="/A087777/b087777.txt">Table of n, a(n) for n = 1..10000</a>
%H A087777 B. Balamohan, A. Kuznetsov and S. Tanny, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Tanny/tanny3.html">On the behavior of a variant of Hofstadter's Q-sequence</a>, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
%H A087777 Nathan Fox, <a href="https://arxiv.org/abs/1611.08244">A Slow Relative of Hofstadter's Q-Sequence</a>, arXiv:1611.08244 [math.NT], 2016.
%H A087777 D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; <a href="https://vimeo.com/91708646">Part 1</a>, <a href="https://vimeo.com/91710600">Part 2</a>.
%H A087777 D. R. Hofstadter, <a href="/A087777/a087777.pdf">Plot of first 100000 terms</a>
%H A087777 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A087777 a := proc(n) option remember; if n<=4 then 1 else if n > a(n-2) and n > a(n-4) then RETURN(a(n-a(n-2))+a(n-a(n-4))); else ERROR(" died at n= ", n); fi; fi; end;
%t A087777 a[n_] := a[n] = If[n <= 4, 1, a[n - a[n - 2]] + a[n - a[n - 4]]];
%t A087777 Array[a, 80] (* _Jean-François Alcover_, Nov 24 2017 *)
%o A087777 (Magma) [n le 4 select 1 else Self(n-Self(n-2))+Self(n-Self(n-4)): n in [1..80]]; // _Vincenzo Librandi_, Sep 10 2016
%Y A087777 Cf. A005185 (Q(1,2)), A063882 (Q(1,4)), A046700.
%K A087777 nonn
%O A087777 1,5
%A A087777 _Roger L. Bagula_, Oct 05 2003
%E A087777 Edited by _N. J. A. Sloane_, Nov 06 2007