A046702 a(n)=a(n-a(n-1))+a(n-1-a(n-2))+a(n-2-a(n-3)), n>3. a(1)=a(2)=a(3)=1.

1, 1, 1, 3, 3, 3, 5, 5, 7, 5, 7, 7, 9, 9, 9, 11, 11, 13, 11, 15, 13, 17, 13, 17, 15, 19, 17, 19, 17, 21, 19, 23, 19, 23, 21, 25, 23, 25, 25, 27, 27, 27, 29, 29, 31, 29, 33, 31, 35, 31, 37, 33, 39, 33, 41, 35, 43, 35, 43, 37, 45, 39, 45, 39, 47, 41, 49, 41, 49, 43, 51, 45, 51, 45

Offset: 1

Author

R. K. Guy

Keywords

• nonn
• look

References

• Sequence proposed by Reg Allenby.
• Callaghan, Joseph, John J. Chew III, and Stephen M. Tanny. "On the behavior of a family of meta-Fibonacci sequences." SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See T_{0,3} with initial values 1,1,1, as in Fig. 1.6. - N. J. A. Sloane, Apr 16 2014

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A240833, A240834.

Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.

Programs

Maple

#T_s,k(n) from Callaghan et al. Eq. (1.6). - From N. J. A. Sloane, Apr 16 2014
s:=0; k:=3;
a:=proc(n) option remember; global s,k;
if n <= 2 then 1
elif n = 3 then 1
else
    add(a(n-i-s-a(n-i-1)),i=0..k-1);
fi; end;
t1:=[seq(a(n),n=1..100)];

Mathematica

a[n_] := a[n] = a[n-a[n-1]] + a[n-1-a[n-2]] + a[n-2-a[n-3]]; a[1] = a[2] = a[3] = 1; Array[a, 80] (* Jean-François Alcover, Dec 12 2016 *)

Extensions

Corrected and extended by Michael Somos