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A367953 Fixed point of the morphism 2 -> {2,2,4}, t -> {t-2,t,t,t+2} (for t > 2), starting from {2}.

%I A367953 #25 Jun 12 2024 03:13:48
%S A367953 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 A367953 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 A367953 6,8,2,2,4,2,2,4,2,4,4,6,2,2,4,2,4,4,6,2,4,4
%N A367953 Fixed point of the morphism 2 -> {2,2,4}, t -> {t-2,t,t,t+2} (for t > 2), starting from {2}.
%C A367953 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 A367953 Paolo Xausa, <a href="/A367953/b367953.txt">Table of n, a(n) for n = 1..24310</a> (first 8 iterations).
%t A367953 Nest[Flatten[ReplaceAll[#,{2->{2,2,4},t_/;t>2:>{t-2,t,t,t+2}}]]&,{2},5]
%o A367953 (Python)
%o A367953 from itertools import islice
%o A367953 def A367953_gen(): # generator of terms
%o A367953     a, l = [2], 0
%o A367953     while True:
%o A367953         yield from a[l:]
%o A367953         c = sum(([2,2,4] if d==2 else [d-2,d,d,d+2] for d in a), start=[])
%o A367953         l, a = len(a), c
%o A367953 A367953_list = list(islice(A367953_gen(),30)) # _Chai Wah Wu_, Dec 26 2023
%Y A367953 Cf. A001700, A363718, A367508, A367951.
%K A367953 nonn
%O A367953 1,1
%A A367953 _Paolo Xausa_, Dec 05 2023