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k appears t+1 times, where t is the number of trailing zeros in A324474(k).
4

%I #14 Mar 14 2021 20:45:05

%S 1,2,3,3,4,4,5,5,5,6,7,7,7,8,9,9,9,9,10,11,12,12,13,13,13,13,14,15,16,

%T 16,17,17,17,17,17,18,19,20,20,21,21,22,22,22,23,24,24,24,24,24,25,26,

%U 27,27,28,28,29,29,29,30,31,31,31,31,31,31,32,33,34,34

%N k appears t+1 times, where t is the number of trailing zeros in A324474(k).

%C Interesting because the recurrence is nested one layer deeper than the recurrences for A046699 and A316628.

%H Rémy Sigrist, <a href="/A324475/b324475.txt">Table of n, a(n) for n = 1..10000</a>

%H Nathan Fox, <a href="https://vimeo.com/322291024">Trees, Fibonacci Numbers, and Nested Recurrences</a>, Rutgers University Experimental Math Seminar, Mar 07, 2019

%H Rémy Sigrist, <a href="/A324475/a324475.gp.txt">PARI program for A324475</a>

%F For n>3, a(n) = a(n-a(n-1)) + a(n-1-a(n-2)-a(n-2-a(n-2))) + a(n-2-a(n-3)-a(n-3-a(n-3)) - a(n-3-a(n-3)-a(n-3-a(n-3)))). - _Nathan Fox_, Mar 09 2019 (This formula assumes that a(0) = 0. - _Rémy Sigrist_, Mar 14 2021)

%o (PARI) See Links section.

%Y Cf. A324474.

%Y A046699, A316628, A324473, A324477 have similar definitions.

%K nonn,base

%O 1,2

%A _Nathan Fox_ and _N. J. A. Sloane_, Mar 09 2019

%E Data corrected and more terms from _Rémy Sigrist_, Mar 14 2021