A352956 For n>1, a(n) = a(n - a(n-1)) + a(n-2) starting with a(0) = a(1) = 1.

1, 1, 2, 2, 4, 3, 6, 4, 10, 5, 13, 6, 19, 7, 23, 8, 33, 9, 38, 10, 51, 11, 57, 12, 76, 13, 83, 14, 106, 15, 114, 16, 147, 17, 156, 18, 194, 19, 204, 20, 255, 21, 266, 22, 323, 23, 335, 24, 411, 25, 424, 26, 507, 27, 521, 28, 627, 29, 642, 30, 756, 31, 772, 32, 919, 33, 936

Offset

0,3

Links

Table of n, a(n) for n=0..66.

Bartosz Sobolewski and Maciej Ulas, Solutions of certain meta-Fibonacci recurrences, arXiv:2204.04011 [math.NT], 2022.

Formula

a(2*k+1) = k+1; a(2*k+2) = a(2*k) + a(k+1). See arXiv link.

Mathematica

a[n_?(# < 2 &)] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - 2];  Array[a, 100, 0] (* Amiram Eldar, Apr 11 2022 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(x=n - va[n-1]); va[n] = if (x<=0, 1, va[x]) + if (n<=2, 1, va[n-2]); ); concat(1, va); }
(Python)
from functools import cache
@cache
def a(n): return 1 if n <= 1 else a(n-a(n-1)) + a(n-2)
print([a(n) for n in range(67)]) # Michael S. Branicky, Apr 11 2022

Crossrefs

Sequence in context: A029578 A054345 A368582 * A304214 A060367 A267451

Adjacent sequences: A352953 A352954 A352955 * A352957 A352958 A352959

Keyword

nonn

Author

Michel Marcus, Apr 11 2022

Status

approved