A240833 -id:A240833 - cp's OEIS frontend

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

R. K. Guy

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

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

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.

#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)];

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 *)

Corrected and extended by Michael Somos

A240834 Sequence R(n) arising from analysis of structure of A046702.

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 4, 3, 4, 3, 6, 5, 6, 5, 6, 7, 6, 7, 6, 9, 6, 9, 6, 11, 8, 11, 8, 11, 10, 13, 10, 13, 10, 15, 12, 15, 12, 15, 14, 15, 14, 15, 16, 15, 16, 15, 18, 15, 18, 15, 20, 15, 20, 15, 22, 15, 22, 15, 24, 17, 24, 17, 24, 19, 26, 19, 26, 19, 28, 21, 28, 21, 28, 23, 30, 23, 30, 23, 32, 23, 32, 23, 34, 25, 34, 25, 34

Offset: 1

N. J. A. Sloane, Apr 16 2014

nonn

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 Eq. (3.1) and Table 3.1.

Index entries for Hofstadter-type sequences

Cf. A046702, A240833.

#T_s,k(n) from Callaghan et al. Eq. (3.1).
s:=0; k:=3;
T:=proc(n) option remember; global R,U,s,k; # A046702
if n <= s+k then 1
else
add(U(n-i),i=0..k-1);
fi; end;
U:=proc(n) option remember; global R,T,s,k; # A240833
T(R(n)); end;
R:=proc(n) option remember; global U,T,s,k; # A240834
n-s-T(n-1); end;
t1:=[seq(R(n),n=1..100)];

cp's OEIS Frontend

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.

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