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

%I A240832 #18 Dec 06 2023 15:29:48
%S A240832 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,
%T A240832 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,
%U A240832 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
%N A240832 Sequence R(n) arising from analysis of structure of A240830.
%H A240832 Paolo Xausa, <a href="/A240832/b240832.txt">Table of n, a(n) for n = 1..10000</a>
%H A240832 Joseph Callaghan, John J. Chew III, and Stephen M. Tanny, <a href="https://doi.org/10.1137/S0895480103421397">On the behavior of a family of meta-Fibonacci sequences</a>, SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See Eq. (2.2) and Table 2.3.
%H A240832 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240832 #T_s,k(n) from Callaghan et al. Eq. (2.2).
%p A240832 s:=0; k:=7;
%p A240832 T:=proc(n) option remember; global R,U,s,k; # A240830
%p A240832 if n <= s+k then 1
%p A240832 else
%p A240832 add(U(n-i),i=0..k-1);
%p A240832 fi; end;
%p A240832 U:=proc(n) option remember; global R,T,s,k; # A240831
%p A240832 T(R(n)); end;
%p A240832 R:=proc(n) option remember; global U,T,s,k; # A240832
%p A240832 n-s-T(n-1); end;
%p A240832 t1:=[seq(R(n),n=1..100)];
%t A240832 A240830[n_]:=A240830[n]=If[n<=7,1,Sum[A240830[A240832[n-i]],{i,0,6}]];
%t A240832 A240832[n_]:=A240832[n]=n-A240830[n-1];
%t A240832 Array[A240832,100] (* _Paolo Xausa_, Dec 06 2023, after _N. J. A. Sloane_ *)
%Y A240832 Cf. A240830, A240831.
%K A240832 nonn
%O A240832 1,3
%A A240832 _N. J. A. Sloane_, Apr 16 2014