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A367951 Fixed point of the morphism 1 -> {1,3}, t -> {t-2,t,t,t+2} (for t > 1), starting from {1}.

%I A367951 #30 Jun 12 2024 03:13:40
%S A367951 1,3,1,3,3,5,1,3,1,3,3,5,1,3,3,5,3,5,5,7,1,3,1,3,3,5,1,3,1,3,3,5,1,3,
%T A367951 3,5,3,5,5,7,1,3,1,3,3,5,1,3,3,5,3,5,5,7,1,3,3,5,3,5,5,7,3,5,5,7,5,7,
%U A367951 7,9,1,3,1,3,3,5,1,3,1,3,3,5,1,3,3,5,3,5,5,7
%N A367951 Fixed point of the morphism 1 -> {1,3}, t -> {t-2,t,t,t+2} (for t > 1), starting from {1}.
%C A367951 The first binomial(2*k,k) = A000984(k) terms (k >= 1) are the row lengths of the Christmas tree pattern (A367508) of order 2*k. See A367953 for the morphism that generates row lengths for odd orders.
%D A367951 Donald E. Knuth, The Art of Computer Programming, Vol. 4A: Combinatorial Algorithms, Part 1, Addison-Wesley, 2011, Section 7.2.1.6, exercise 76, pp. 479 and 800.
%H A367951 Paolo Xausa, <a href="/A367951/b367951.txt">Table of n, a(n) for n = 1..12870</a> (first 8 iterations).
%t A367951 Nest[Flatten[ReplaceAll[#, {1->{1, 3}, t_/;t>1:>{t-2, t, t, t+2}}]]&, {1}, 5]
%o A367951 (Python)
%o A367951 from itertools import islice
%o A367951 def A367951_gen(): # generator of terms
%o A367951     a, l = [1], 0
%o A367951     while True:
%o A367951         yield from a[l:]
%o A367951         c = sum(([1, 3] if d==1 else [d-2,d,d,d+2] for d in a), start=[])
%o A367951         l, a = len(a), c
%o A367951 A367951_list = list(islice(A367951_gen(),30)) # _Chai Wah Wu_, Dec 26 2023
%Y A367951 Cf. A000984, A363718, A367508, A367953.
%K A367951 nonn
%O A367951 1,2
%A A367951 _Paolo Xausa_, Dec 05 2023