A354856 a(1) = 1, a(n) = the number of times a(n-1) appears among the first n-2 terms.

1, 0, 0, 1, 1, 2, 0, 2, 1, 3, 0, 3, 1, 4, 0, 4, 1, 5, 0, 5, 1, 6, 0, 6, 1, 7, 0, 7, 1, 8, 0, 8, 1, 9, 0, 9, 1, 10, 0, 10, 1, 11, 0, 11, 1, 12, 0, 12, 1, 13, 0, 13, 1, 14, 0, 14, 1, 15, 0, 15, 1, 16, 0, 16, 1, 17, 0, 17, 1, 18, 0, 18, 1, 19, 0, 19, 1, 20, 0, 20

Offset: 1

Author

Eric Fox, Jun 09 2022

Keywords

• nonn

Examples

			a(10) = 3 because a(9) = 1 and 3 other 1s appear before that.
		

Crossrefs

Cf. A342585, A347317.

Programs

PARI

lista(nn) = my(va=vector(nn)); va[1] = 1; for (n=2, nn, my(vb = vector(n-2, k, va[k])); va[n] = #select(x->(x==va[n-1]), vb);); va; \\ Michel Marcus, Jun 13 2022

Python

from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    anprev, an, inventory = None, 1, Counter()
    for n in count(2):
        yield an
        anprev, an = an, inventory[an]
        inventory[anprev] += 1
print(list(islice(agen(), 80))) # Michael S. Branicky, Jun 09 2022

Formula

a(4n+1..4n+4) = 1, n+1, 0, n+1 for n >= 1. - Michael S. Branicky, Jun 12 2022

Extensions

a(54) and beyond from Michael S. Branicky, Jun 12 2022