A240831 -id:A240831 - cp's OEIS frontend

A240830 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=7.

1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 13, 13, 13, 13, 13, 13, 19, 13, 19, 19, 19, 19, 25, 19, 25, 19, 25, 25, 31, 25, 31, 25, 31, 25, 31, 31, 37, 31, 37, 31, 37, 37, 37, 37, 43, 37, 43, 43, 43, 43, 43, 43, 49, 49, 49, 49, 49, 49, 49, 55, 55, 55, 55, 55, 55, 61, 55, 61, 61, 61, 61, 67, 61, 67, 61, 67, 67, 73

Offset: 1

N. J. A. Sloane, Apr 16 2014

N. J. A. Sloane, Table of n, a(n) for n = 1..20000
Joseph Callaghan, 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 Table 2.1.
Index entries for Hofstadter-type sequences

Same recurrence as A240828, A120503 and A046702.
See also A240831, A240832.
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. (1.7).
s:=0; k:=7;
a:=proc(n) option remember; global s,k;
if n <= s+k 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)];

A240830[n_]:=A240830[n]=If[n<=7,1,Sum[A240830[n-i-A240830[n-i-1]],{i,0,6}]];
Array[A240830,100] (* Paolo Xausa, Dec 06 2023 *)

A240832 Sequence R(n) arising from analysis of structure of A240830.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 3, 10, 5, 6, 7, 8, 3, 10, 5, 12, 7, 8, 3, 10, 5, 12, 7, 14, 9, 10, 5, 12, 7, 14, 9, 10, 11, 12, 7, 14, 9, 10, 11, 12, 13, 14, 9, 10, 11, 12, 13, 14, 15, 10, 11, 12, 13, 14, 15, 10, 17, 12, 13, 14, 15, 10, 17, 12, 19, 14, 15, 10, 17, 12, 19, 14, 21, 10, 17

Offset: 1

N. J. A. Sloane, Apr 16 2014

nonn

Paolo Xausa, Table of n, a(n) for n = 1..10000
Joseph Callaghan, 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. (2.2) and Table 2.3.
Index entries for Hofstadter-type sequences

Cf. A240830, A240831.

#T_s,k(n) from Callaghan et al. Eq. (2.2).
s:=0; k:=7;
T:=proc(n) option remember; global R,U,s,k; # A240830
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; # A240831
T(R(n)); end;
R:=proc(n) option remember; global U,T,s,k; # A240832
n-s-T(n-1); end;
t1:=[seq(R(n),n=1..100)];

A240830[n_]:=A240830[n]=If[n<=7,1,Sum[A240830[A240832[n-i]],{i,0,6}]];
A240832[n_]:=A240832[n]=n-A240830[n-1];
Array[A240832,100] (* Paolo Xausa, Dec 06 2023, after N. J. A. Sloane *)

cp's OEIS Frontend

A240830 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=7.

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