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A240831 Sequence U(n) arising from analysis of structure of A240830.

%I A240831 #23 Dec 06 2023 14:20:43
%S A240831 1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,7,1,7,1,1,1,7,1,7,1,7,1,7,1,7,
%T A240831 1,7,1,7,7,7,1,7,1,7,7,7,7,7,1,7,7,7,7,7,7,7,7,7,7,7,7,7,13,7,7,7,7,7,
%U A240831 13,7,13,7,7,7,13,7,13,7,13,7,13,7,13,7,13,7,19,7,13,7,13,7,19,7,19,7,13,7,19
%N A240831 Sequence U(n) arising from analysis of structure of A240830.
%H A240831 Paolo Xausa, <a href="/A240831/b240831.txt">Table of n, a(n) for n = 2..10000</a>
%H A240831 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 2.2.
%H A240831 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240831 #T_s,k(n) from Callaghan et al. Eq. (2.2).
%p A240831 s:=0; k:=7;
%p A240831 T:=proc(n) option remember; global R,U,s,k; # A240830
%p A240831 if n <= s+k then 1
%p A240831 else
%p A240831     add(U(n-i),i=0..k-1);
%p A240831 fi; end;
%p A240831 U:=proc(n) option remember; global R,T,s,k; # A240831
%p A240831 T(R(n)); end;
%p A240831 R:=proc(n) option remember; global U,T,s,k; # A240832
%p A240831 n-s-T(n-1); end;
%p A240831 t1:=[seq(U(n),n=2..100)];
%t A240831 A240830[n_]:=A240830[n]=If[n<=7,1,Sum[A240831[n-i],{i,0,6}]];
%t A240831 A240831[n_]:=A240831[n]=A240830[n-A240830[n-1]];
%t A240831 Array[A240831,100,2] (* _Paolo Xausa_, Dec 06 2023, after _N. J. A. Sloane_ *)
%Y A240831 Cf. A240830, A240832.
%K A240831 nonn
%O A240831 2,14
%A A240831 _N. J. A. Sloane_, Apr 16 2014