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

1,5

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A114431 A167689 A058184 * A030118 A331379 A023835

Adjacent sequences: A087774 A087775 A087776 * A087778 A087779 A087780

Keyword

nonn

Author

Roger L. Bagula, Oct 05 2003

Extensions

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

Status

approved