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A318056 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n-1)) where t = A004001. a(n) = 2*b(n) - n.

%I A318056 #11 Aug 18 2018 05:23:30
%S A318056 1,0,-1,0,1,0,1,0,-3,-2,-3,-2,-1,0,-1,0,5,4,5,4,5,2,1,2,3,4,3,0,1,0,1,
%T A318056 0,-11,-10,-11,-10,-11,-10,-7,-6,-7,-6,-9,-10,-9,-8,-7,-8,-3,-4,-3,-2,
%U A318056 -1,-2,-5,-4,-5,-4,-1,0,-1,0,-1,0,21,20,21,20,21,20,21,16,15,16,15,16,19,20,19,20
%N A318056 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n-1)) where t = A004001. a(n) = 2*b(n) - n.
%H A318056 Altug Alkan, <a href="/A318056/b318056.txt">Table of n, a(n) for n = 1..32768</a>
%H A318056 Altug Alkan, <a href="/A318056/a318056.png">Line plot of a(n) for n <= 2^17</a>
%p A318056 t:= proc(n) option remember; `if`(n<3, 1,
%p A318056       t(t(n-1)) +t(n-t(n-1)))
%p A318056     end:
%p A318056 b:= proc(n) option remember; `if`(n<3, 1,
%p A318056       n -b(t(n)) -b(n-t(n-1)))
%p A318056     end:
%p A318056 seq(2*b(n)-n, n=1..100); # after _Alois P. Heinz_ at A317686
%t A318056 t[1]=t[2]=1; t[n_] := t[n] = t[t[n-1]] + t[n - t[n-1]]; b[1]=b[2]=1; b[n_] := b[n] = n - b[t[n]] - b[n - t[n-1]]; a[n_] := 2*b[n] - n; Array[a, 95] (* after _Giovanni Resta_ at A317854 *)
%o A318056 (PARI) t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[n] = t[n-t[n-1]]+t[t[n-1]]); b=vector(99); b[1]=b[2]=1; for(n=3, #b, b[n] = n-b[t[n]]-b[n-t[n-1]]);vector(99, k, 2*b[k]-k)
%Y A318056 Cf. A004001, A317754, A317854.
%K A318056 sign,look
%O A318056 1,9
%A A318056 _Altug Alkan_, Aug 14 2018