A300623 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.

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, -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, -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

Offset: 1

Author

Altug Alkan, Aug 14 2018

Keywords

• sign
• look

Comments

Sequence has a fractal-like structure. Fibonacci numbers (A000045) are determinative for the generational boundaries.

Links

• Altug Alkan, Table of n, a(n) for n = 1..28657
• Altug Alkan, Line plot of a(n) for n <= 28657
• Altug Alkan, Scatterplot of a(n) for n <= 75025

Crossrefs

Cf. A302128, A318056.

Programs

Maple

t:= proc(n) option remember; `if`(n<4, 1,
      t(t(n-2)) +t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<2, 1,
      n -b(t(n)) -b(n-t(n-1)))
    end:
seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686

Mathematica

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 *)

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)