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A188428 Number of strings of length n on three symbols containing all permutations of those three symbols as substrings (factors), divided by six. 3
0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 54, 276, 1282, 5585, 23223, 93146, 362928, 1380535, 5145692, 18846775, 67982489, 241940204, 850777688, 2959796467, 10197732687, 34828459508, 118003182174, 396897710483, 1326018464696, 4402883891950, 14536059784925, 47737688829399 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Division by six is performed so that strings that are identical up to swapping the symbols are not double-counted.

The corresponding sequence for strings of length n on two symbols is given by a(n) = 2^(n-1) - n = A000295(n-1).

LINKS

Paul Tek, Table of n, a(n) for n = 1..2000

Paul Tek, PERL program for this sequence

EXAMPLE

a(9) = 1 because there are 6 strings of length 9 on the three symbols "1", "2", and "3" containing each of "123", "132", "213", "231", "312", and "321" as substrings: they are "123121321" and the five other strings obtained by swapping the roles of "1", "2", and "3" in that string.

The substrings must be contiguous -- if they were allowed to be non-contiguous (i.e., subsequences) then there would be a valid string of length 7: "1232132" (see A062714).

CROSSREFS

Cf. A000295, A062714, A180632, A224986.

Sequence in context: A027472 A022637 A001392 * A243415 A276602 A079764

Adjacent sequences:  A188425 A188426 A188427 * A188429 A188430 A188431

KEYWORD

nonn

AUTHOR

Nathaniel Johnston, Mar 30 2011

STATUS

approved

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Last modified October 17 12:50 EDT 2018. Contains 316280 sequences. (Running on oeis4.)