A352956 - OEIS

%I #21 Jun 07 2022 11:13:00

%S 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,

%T 14,106,15,114,16,147,17,156,18,194,19,204,20,255,21,266,22,323,23,

%U 335,24,411,25,424,26,507,27,521,28,627,29,642,30,756,31,772,32,919,33,936

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

%H Bartosz Sobolewski and Maciej Ulas, <a href="https://arxiv.org/abs/2204.04011">Solutions of certain meta-Fibonacci recurrences</a>, arXiv:2204.04011 [math.NT], 2022.

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

%t 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 *)

%o (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);}

%o (Python)

%o from functools import cache

%o @cache

%o def a(n): return 1 if n <= 1 else a(n-a(n-1)) + a(n-2)

%o print([a(n) for n in range(67)]) # _Michael S. Branicky_, Apr 11 2022

%K nonn

%O 0,3

%A _Michel Marcus_, Apr 11 2022