A283717 Number of distinct subsets S of {t,t+1,...,m-1}, t = ceiling(m/2), such that number of distinct symbols in the "most general word" of length m having its periods a superset of (S union {m}) is m-n, for m >= 2n.

1, 1, 2, 2, 4, 3, 8, 6, 15, 8, 32, 13, 62, 19, 123, 34, 249, 35, 506

Offset

1,3

Comments

The period of a word w is the least positive integer p such that w[i] = w[i+p] over all i for which this indexing is defined. The "most general word" is over an arbitrary alphabet that can be taken to be {1,2,...,m}. For example, the "most general word" of length 10 with periods {6,9,10} is 1231451231.

Links

Table of n, a(n) for n=1..19.

Example

For n = 5 the four possible sets of periods are {m-5}, {m-1,m-4}, {m-2,m-3}, and {m-1,m-2,m-3}. The corresponding "most general words" are 123...(m-5)12345, 1231456...(m-5)1231, 1112345...(m-5)111, 1112345...(m-5)111, all of which have largest element m-5.

Crossrefs

Cf. A005434.

Sequence in context: A056429 A133806 A360241 * A185333 A005176 A050335

Adjacent sequences: A283714 A283715 A283716 * A283718 A283719 A283720

Keyword

nonn,more

Author

Jeffrey Shallit, Mar 15 2017

Status

approved