

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
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OFFSET

1,10


COMMENTS

Division by six is performed so that strings that are identical up to swapping the symbols are not doublecounted.
The corresponding sequence for strings of length n on two symbols is given by a(n) = 2^(n1)  n = A000295(n1).


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 noncontiguous (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



