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A227145
Numbers satisfying an infinite nested recurrence relation.
2
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
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
KEYWORD
nonn
AUTHOR
Frank Ruskey, Jul 04 2013
STATUS
approved