A046700 a(1) = a(2) = a(3) = 1, a(n) = a(n - a(n-1)) + a(n - a(n-3)) for 3 < n < 165.

1, 1, 1, 2, 3, 4, 4, 5, 5, 7, 6, 8, 7, 9, 8, 10, 9, 12, 9, 12, 10, 15, 11, 16, 12, 17, 13, 18, 14, 19, 15, 21, 17, 18, 18, 21, 19, 21, 24, 20, 22, 24, 20, 31, 19, 30, 19, 28, 19, 30, 21, 32, 21, 34, 21, 36, 21, 38, 21, 48, 18, 53, 15, 49, 18, 49, 24, 61, 17, 51, 19, 42

Offset: 1

Author

R. K. Guy

Keywords

• nonn
• fini
• full

References

• Sequence proposed by Reg Allenby.
• Undefined past a(164), since a(164) = 202.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..164 [The full sequence]
• 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.
• Index entries for Hofstadter-type sequences

Programs

Maple

V := proc(n) option remember; if n<=3 then 1 else if n > V(n-1) and n > V(n-3) then RETURN(V(n-V(n-1))+V(n-V(n-3))); else ERROR(" died at n= ", n); fi; fi; end;

Mathematica

a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 3]]; Array[a, 72] (* Jean-François Alcover, Dec 12 2016 *)

Extensions

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