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%I #25 Sep 07 2018 03:15:06
%S 1,-2,1,0,1,-2,-1,-2,1,2,-1,0,1,0,1,-2,-1,2,3,2,1,-2,-1,-4,-3,2,3,0,1,
%T -4,-3,-4,-3,-2,1,2,-1,0,5,6,3,4,-5,-4,-7,-6,-3,-2,-3,2,3,2,3,2,1,0,1,
%U -2,-1,4,5,2,3,-8,-7,-10,-9,-4,-3,-6,-5,8,9,6,7,10,11,10,5,6,5,6,-1,0,-1,0,-1,0,1,-2,-1,-4,-3
%N Let b(1) = 1; for n >= 2, b(n) = n - b(t(n)) - b(n-t(n-1)) where t = A302128. a(n) = 2*b(n) - n.
%C Sequence has a fractal-like structure. Fibonacci numbers (A000045) are determinative for the generational boundaries.
%H Altug Alkan, <a href="/A300623/b300623.txt">Table of n, a(n) for n = 1..28657</a>
%H Altug Alkan, <a href="/A300623/a300623.png">Line plot of a(n) for n <= 28657</a>
%H Altug Alkan, <a href="/A300623/a300623_1.png">Scatterplot of a(n) for n <= 75025</a>
%p t:= proc(n) option remember; `if`(n<4, 1,
%p t(t(n-2)) +t(n-t(n-1)))
%p end:
%p b:= proc(n) option remember; `if`(n<2, 1,
%p n -b(t(n)) -b(n-t(n-1)))
%p end:
%p seq(2*b(n)-n, n=1..100); # after _Alois P. Heinz_ at A317686
%t t[1]=t[2]=t[3]=1; t[n_] := t[n] = t[t[n-2]] + t[n - t[n-1]]; b[1]=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 (PARI) t=vector(99); t[1]=t[2]=t[3]=1; for(n=4, #t, t[n] = t[n-t[n-1]]+t[t[n-2]]); b=vector(99); b[1]=1; for(n=2, #b, b[n] = n-b[t[n]]-b[n-t[n-1]]); vector(99,k, 2*b[k]-k)
%Y Cf. A302128, A318056.
%K sign,look
%O 1,2
%A _Altug Alkan_, Aug 14 2018
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