

A289671


Consider the Post tag system defined in A284116; a(n) = number of binary words of length n which terminate in a cycle.


15



0, 2, 4, 8, 16, 48, 64, 128, 320, 704, 1536, 3328, 5632, 9728, 20480, 44032, 94208, 180224, 348160, 720896, 1458176, 2801664, 6062080, 12582912, 23986176, 49807360, 103809024, 202899456, 415760384, 853540864, 1663041536
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OFFSET

1,2


COMMENTS

For n such that no binary word of length n has an infinite orbit under the Post tag system (cf. A284116), which includes all n <= 57, a(n) + A289670(n) = 2^n.


LINKS

Don Reble, Table of n, a(n) for n = 1..57


EXAMPLE

For length n=2, there are two words which cycle, 10 and 11: 10 > 101 > 1101 > 11101 > 011101 > 10100 > 001101 > 10100, which has entered a cycle.


MAPLE

See A289670.


MATHEMATICA

Table[ne = 0;
For[i = 0, i < 2^n, i++, lst = {};
w = IntegerString[i, 2, n];
While[! MemberQ[lst, w],
AppendTo[lst, w];
If[w == "", ne++; Break[]];
If[StringTake[w, 1] == "0", w = StringDrop[w <> "00", 3],
w = StringDrop[w <> "1101", 3]]]];
2^n  ne, {n, 1, 12}] (* Robert Price, Sep 26 2019 *)


CROSSREFS

Cf. A284116, A284119, A284121, A289670A289674.
A289675 lists the initial words that terminate at the empty string.
Sequence in context: A255394 A081473 A018627 * A096853 A027155 A129335
Adjacent sequences: A289668 A289669 A289670 * A289672 A289673 A289674


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Jul 29 2017


STATUS

approved



