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A330448 a(n) = A330447(n) - A316905(n).

%I A330448 #14 Nov 13 2023 07:27:44
%S A330448 0,0,0,0,1,0,0,0,8,0,4,0,0,3,0,0,0,0,0,0,23,0,45,0,0,0,74,8,0,56,47,0,
%T A330448 0,105,67,85,64,0,130,45,111,0,21,136,74,98,0,97,0,0,35,0,0,0,37,0,0,
%U A330448 0,52,0,104,52,67,0,0,70,0,0,0,0,0,152,0,0,0,0,0
%N A330448 a(n) = A330447(n) - A316905(n).
%H A330448 Alois P. Heinz, <a href="/A330448/b330448.txt">Table of n, a(n) for n = 0..20000</a>
%p A330448 b:= proc() 0 end:
%p A330448 g:= proc(n) option remember; local t;
%p A330448       t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
%p A330448       b(t):= b(t)+1; t
%p A330448     end:
%p A330448 f:= proc() local t, a; t, a:= -1, proc() -1 end;
%p A330448       proc(n) local h;
%p A330448         while a(n) = -1 do
%p A330448           t:= t+1; h:= g(t);
%p A330448           if a(h) = -1 then a(h):= t fi
%p A330448         od; a(n)
%p A330448       end
%p A330448     end():
%p A330448 h:= proc(n) option remember; `if`(n<0, 0,
%p A330448       max(h(n-1), f(n)))
%p A330448     end:
%p A330448 a:= n-> h(n)-f(n):
%p A330448 seq(a(n), n=0..100);
%t A330448 b[_] = 0;
%t A330448 g[n_] := g[n] = Module[{t}, t = If[n < 2, n, b[g[n - 1]] + b[g[n - 2]]]; b[t] = b[t] + 1; t];
%t A330448 f[n_] := Module[{t, a}, t = -1; a[_] = -1; Module[{h}, While[a[n] == -1, t = t + 1; h = g[t]; If[a[h] == -1, a[h] = t]]; a[n]]];
%t A330448 h[n_] := h[n] = If[n < 0, 0, Max[h[n - 1], f[n]]];
%t A330448 a[n_] := h[n] - f[n];
%t A330448 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 13 2023, after _Alois P. Heinz_ *)
%Y A330448 Cf. A316774, A316905, A330447.
%K A330448 nonn,look
%O A330448 0,9
%A A330448 _Alois P. Heinz_, Dec 15 2019