A060688 Number of dissimilar ternary squarefree words of length n+1.

1, 2, 3, 5, 7, 10, 13, 18, 24, 34, 44, 57, 76, 103, 133, 174, 232, 305, 398, 530, 691, 903, 1172, 1533, 1982, 2581, 3370, 4404, 5737, 7477, 9741, 12687, 16546, 21586, 28091, 36586, 47625, 62034, 80741, 105111, 136859, 178252

Offset

1,2

Comments

Cycle b-> c-> b and a-> b-> c-> a to get 6 similar words in A006156(n+1).

References

N. Wirth, Systematisches Programmieren, 1975, ch. 15.4, table 15.68

Links

Table of n, a(n) for n=1..42.

Robert Shelton, Aperiodic words on three symbols, J. Reine Angew. Math. 321 (1981), 195--209. MR0597989 (82m:05004a). See Table 1 on page 207. - N. J. A. Sloane, Jun 22 2014

Formula

a(n) = A006156(n+1)/6. [corrected by Michel Marcus, Nov 26 2020]

Example

ab~ac (cycle b,c), ab~bc~ca and ac~ba~cb (cycle a,b,c) => a(1) = 6/6 = 1.

Mathematica

(* This program is not convenient for a large number of terms *) a[n_] := a[n] = (1/6)*Length[ DeleteCases[ Tuples[ Range[3], n + 1], {a___, b__, b__, c___}]]; Reap[ Do[ Print["a[", n, "] = ", a[n]]; Sow[a[n]], {n, 1, 12}]][[2, 1]] (* Jean-François Alcover, Jul 24 2013 *)

Crossrefs

Cf. A006156.

Sequence in context: A088318 A038083 A238863 * A005691 A035954 A023192

Adjacent sequences: A060685 A060686 A060687 * A060689 A060690 A060691

Keyword

nonn

Author

Frank Ellermann, Apr 19 2001

Status

approved