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Fixed point of the morphism 2 -> {2,2,4}, t -> {t-2,t,t,t+2} (for t > 2), starting from {2}.
5

%I #25 Jun 12 2024 03:13:48

%S 2,2,4,2,2,4,2,4,4,6,2,2,4,2,2,4,2,4,4,6,2,2,4,2,4,4,6,2,4,4,6,4,6,6,

%T 8,2,2,4,2,2,4,2,4,4,6,2,2,4,2,2,4,2,4,4,6,2,2,4,2,4,4,6,2,4,4,6,4,6,

%U 6,8,2,2,4,2,2,4,2,4,4,6,2,2,4,2,4,4,6,2,4,4

%N Fixed point of the morphism 2 -> {2,2,4}, t -> {t-2,t,t,t+2} (for t > 2), starting from {2}.

%C The first binomial(2*k+1,k+1) = A001700(k) terms (k >= 0) are the row lengths of the Christmas tree pattern (A367508) of order 2*k+1. See A367951 for the morphism that generates row lengths for even orders.

%H Paolo Xausa, <a href="/A367953/b367953.txt">Table of n, a(n) for n = 1..24310</a> (first 8 iterations).

%t Nest[Flatten[ReplaceAll[#,{2->{2,2,4},t_/;t>2:>{t-2,t,t,t+2}}]]&,{2},5]

%o (Python)

%o from itertools import islice

%o def A367953_gen(): # generator of terms

%o a, l = [2], 0

%o while True:

%o yield from a[l:]

%o c = sum(([2,2,4] if d==2 else [d-2,d,d,d+2] for d in a), start=[])

%o l, a = len(a), c

%o A367953_list = list(islice(A367953_gen(),30)) # _Chai Wah Wu_, Dec 26 2023

%Y Cf. A001700, A363718, A367508, A367951.

%K nonn

%O 1,1

%A _Paolo Xausa_, Dec 05 2023