A289671 Consider the Post tag system defined in A284116; a(n) = number of binary words of length n which terminate in a cycle.

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, 3332374528, 6752829440, 13153337344, 26055016448

Offset: 1

Author

N. J. A. Sloane, Jul 29 2017

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A284116, A284119, A284121, A289670-A289674.

A289675 lists the initial words that terminate at the empty string.

Programs

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 *)