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

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, 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, 6, 8, 2, 2, 4, 2, 2, 4, 2, 4, 4, 6, 2, 2, 4, 2, 4, 4, 6, 2, 4, 4

Offset: 1

Author

Paolo Xausa, Dec 05 2023

Keywords

• nonn

Comments

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.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..24310 (first 8 iterations).

Crossrefs

Cf. A001700, A363718, A367508, A367951.

Programs

Mathematica

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

Python

from itertools import islice
def A367953_gen(): # generator of terms
    a, l = [2], 0
    while True:
        yield from a[l:]
        c = sum(([2,2,4] if d==2 else [d-2,d,d,d+2] for d in a), start=[])
        l, a = len(a), c
A367953_list = list(islice(A367953_gen(),30)) # Chai Wah Wu, Dec 26 2023