This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318134 #13 Jul 16 2025 12:10:38
%S A318134 3,15,21,375,108,2427,402,176391,1533,216030,10992,19375935,24612,
%T A318134 13106514
%N A318134 Number of periodic sequences of period 3n generated by the random period doubling substitution 0 --> {01, 10}, 1 --> {00}.
%C A318134 From an initial seed letter 0, the random substitution iteratively acts on words and outputs all possible outcomes from applying all combinations of the allowed substitution rules independently to each letter in a word. So we have:
%C A318134 0 -->
%C A318134 {01, 10} -->
%C A318134 {0100, 1000, 0001, 0010} -->
%C A318134 {01000101, 01000110, 01001001, 01001010, 10000101, 10000110, 10001001, 10001010, 00010101, 00010110, 00011001, 00011010, 00100101, 00100110, 00101001, 00101010, 01010100, 01011000, 01100100, 01101000, 10010100, 10011000, 10100100, 10101000, 01010001, 01010010, 01100001, 01100010, 10010001, 10010010, 10100001, 10100010} --> ...
%C A318134 An infinite sequence is generated by the random substitution if all subwords of the sequence appear as subwords of some word appearing in the infinite list generated above. Some of these infinite sequences will be periodic and so we can enumerate them.
%C A318134 All periodic sequences have period a multiple of 3.
%H A318134 D. Rust, <a href="https://www.math.uni-bielefeld.de/~drust/papers/random_subs_periodic_points.pdf">Periodic points in random substitution subshifts</a>, (2018).
%e A318134 The periodic sequences of length 3 generated by the random period doubling substitution have periodic blocks 001, 010, 100.
%e A318134 The periodic sequences of length 6 generated by the random period doubling substitution have periodic blocks 010100, 101000, 010001, 100010, 000101, 001010, 011000, 110000, 100001, 000011, 000110, 001100, 100100, 001001, 010010.
%Y A318134 Cf. A096268, A275202.
%K A318134 nonn,more
%O A318134 1,1
%A A318134 _Daniel Rust_, Aug 18 2018