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A224986 a(n) = product{k=1,...,n-4} (n-k-2)!^(k*k!). 3
1, 1, 1, 1, 2, 96, 8153726976, 320352637207127391364950814323398779319161580421120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Consider words on n symbols that contain every permutation of those n symbols as contiguous substrings. The minimal length of such a string is conjectured to equal A007489(n) (see A180632). This sequence is a lower bound on the number of distinct (up to relabeling the symbols) such strings of the conjectured minimal length.

It was conjectured in the Ashlock paper that, for all n, there is only one string containing all permutations of length A007489(n). This sequence shows that this conjecture fails as n grows.

REFERENCES

D. Ashlock and J. Tillotson. Construction of small superpermutations and minimal injective superstrings. Congressus Numerantium, 93 (1993), 91-98.

Nathaniel Johnston, The Minimal Superpermutation Problem, http://www.njohnston.ca/2013/04/the-minimal-superpermutation-problem/, 2013.

LINKS

Table of n, a(n) for n=1..8.

N. Johnston. Non-uniqueness of minimal superpermutations. Discrete Math., 313 (2013), 1553-1557.

EXAMPLE

a(n) = 1 for n <= 4, which agrees with the fact that the minimal strings containing all permutations in these cases are unique (see A180632).

MAPLE

seq(product((n-k-2)!^(k*k!), k=1..max(n-4, 0)), n=1..8);

CROSSREFS

Cf. A180632, A188428.

Sequence in context: A091810 A165642 A057528 * A164335 A132206 A139884

Adjacent sequences:  A224983 A224984 A224985 * A224987 A224988 A224989

KEYWORD

nonn,easy

AUTHOR

Nathaniel Johnston, Apr 22 2013

STATUS

approved

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Last modified February 26 12:43 EST 2020. Contains 332280 sequences. (Running on oeis4.)