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

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, 21, 22, 14, 14, 19, 17, 22, 27, 25, 16, 20, 28, 22, 22, 26, 25, 24, 32, 26, 22, 29, 29, 32, 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

Offset: 1

Author

Roger L. Bagula, Oct 05 2003

Keywords

• nonn

Comments

This is the sequence Q(2,4) in the Hofstadter-Huber classification.

It is not known if this sequence is defined for all positive n. Balamohan et al. comment that it shows "inscrutably wild behavior".

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
• Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv:1611.08244 [math.NT], 2016.
• 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; Part 1, Part 2.
• D. R. Hofstadter, Plot of first 100000 terms
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A005185 (Q(1,2)), A063882 (Q(1,4)), A046700.

Programs

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

Maple

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;

Mathematica

a[n_] := a[n] = If[n <= 4, 1, a[n - a[n - 2]] + a[n - a[n - 4]]];
Array[a, 80] (* Jean-François Alcover, Nov 24 2017 *)

Extensions

Edited by N. J. A. Sloane, Nov 06 2007