A337835 a(1) = 0 and for n > 1, a(n+1) = k - a(n) where k is the number of terms equal to a(n) among the first n terms.

0, 1, 0, 2, -1, 2, 0, 3, -2, 3, -1, 3, 0, 4, -3, 4, -2, 4, -1, 4, 0, 5, -4, 5, -3, 5, -2, 5, -1, 5, 0, 6, -5, 6, -4, 6, -3, 6, -2, 6, -1, 6, 0, 7, -6, 7, -5, 7, -4, 7, -3, 7, -2, 7, -1, 7, 0, 8, -7, 8, -6, 8, -5, 8, -4, 8, -3, 8, -2, 8, -1, 8, 0, 9, -8, 9, -7, 9, -6, 9, -5, 9, -4, 9, -3, 9

Offset: 1

Author

Bence Bernáth, Nov 17 2020

Keywords

• sign
• easy

Comments

Empirical observation: -A000194(n) <= a(n) <= A000194(n).

Examples

			For n = 4, a(4) = 2, which appeared only once in the sequence so a(5)=1-2=-1.
		

Links

• Bence Bernáth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000194, A329985.

Programs

MATLAB

length=1000;
sequence(1)=0;
for n=2:1:length
        sequence(n)=nnz(sequence==sequence(end))-sequence(n-1);
end

Mathematica

a = {0}; Do[AppendTo[a, Count[a, a[[-1]]] - a[[-1]]], {100}]; a (* Amiram Eldar, Nov 18 2020 *)
a[1] = 0; a[n_Integer?Positive] := a[n] = Count[Array[a, n - 1], a[n - 1]] - a[n - 1]; Array[a, 101] (* Jan Mangaldan, Nov 27 2020 *)

PARI

lista(nn) = {my(va = vector(nn)); for (n=2, nn, va[n] = #select(x->(x==va[n-1]), vector(n-1, k, va[k])) - va[n-1];); va;} \\ Michel Marcus, Nov 18 2020

Python

from itertools import islice
from collections import Counter
def agen(): # generator of terms
    an, k = 0, Counter()
    while True:
        yield an
        k[an] += 1
        an = k[an] - an
print(list(islice(agen(), 86))) # Michael S. Branicky, Nov 12 2022