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.

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, 0, -11, -10, -11, -10, -11, -10, -7, -6, -7, -6, -9, -10, -9, -8, -7, -8, -3, -4, -3, -2, -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

Offset

1,9

Links

Altug Alkan, Table of n, a(n) for n = 1..32768

Altug Alkan, Line plot of a(n) for n <= 2^17

Maple

t:= proc(n) option remember; `if`(n<3, 1,
      t(t(n-1)) +t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<3, 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]=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 *)

Prog

(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)

Crossrefs

Cf. A004001, A317754, A317854.

Sequence in context: A220344 A176102 A344220 * A096839 A099891 A241173

Adjacent sequences: A318053 A318054 A318055 * A318057 A318058 A318059

Keyword

sign,look

Author

Altug Alkan, Aug 14 2018

Status

approved