A227145 Numbers satisfying an infinite nested recurrence relation.

0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27

Offset

1,4

Comments

Conjecture: a(F_n) = F_{n-2} for n>1, where F_n is the n-th Fibonacci number.

Conjecture: a(n) ~ n*(3-sqrt(5))/2. -Jeffrey Shallit, Oct 12 2022

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Marcel Celaya and Frank Ruskey, Morphic words and nested recurrence relations, arxiv 1307.0153 (Jun 29 2013), [math.CO] (see page 11).

Formula

a(n) = n - 1 - a(n-1) - a(a(n-2)) - a(a(a(n-3))) - a(a(a(a(n-4)))) - ... with a(n) = 0 if n <= 1.

Maple

a:= proc(n) option remember; local i, r, s;
      if n<2 then 0 else r, s:= n, 1;
         for i while s>0 do r, s:= r-s, (a@@i)(n-i) od: r
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 04 2013

Mathematica

a[n_] := a[n]= Which[n <= 1, 0, True, n - 1 -Sum[Nest[a, n - i, i], {i, 1, n}]]; Table[a[i], {i, 0, 30}] (* José María Grau Ribas, Jul 10 2013 *)

Crossrefs

Cf. A060144.

Sequence in context: A278078 A094708 A302931 * A039730 A257807 A152595

Adjacent sequences: A227142 A227143 A227144 * A227146 A227147 A227148

Keyword

nonn

Author

Frank Ruskey, Jul 04 2013

Status

approved