

A192089


Number of permutations of [n] that require a 3letter alphabet in order to be realized by a shift.


0



0, 0, 6, 66, 402, 2028, 8790, 35118, 131982, 475344, 1658382, 5651226, 18912498, 62418180, 203768862, 659487678, 2119617474, 6774043254, 21547968726, 68274910026, 215609878962, 678936947940, 2132568719358, 6683705385078, 20906259913566, 65277851607840
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OFFSET

2,3


COMMENTS

These permutations are those realized by the shift on 3 letters (A192088)
but not by the shift on 2 letters (A059413).


REFERENCES

S. Elizalde, The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765786.


LINKS

Table of n, a(n) for n=2..27.
Sergi Elizalde, The number of permutations realized by a shift, arXiv:0909.2274v1 [math.CO]


FORMULA

a(n)=3^(n2)+sum(psi_3(t)*3^(nt1),t=1..n1)n*sum(psi_2(t)*2^(nt1),t=0..n1), where psi_N(t) is the number of primitive words of length t over an Nletter alphabet, which is expressible in terms of the MÃ¶bius function.


EXAMPLE

a(4)=6 because the permutations 1423, 3241, 4132, 2314 3421, 2134 are the only ones of length 4 that require 3 letters in order to be realized by a shift


CROSSREFS

Equals A192088 minus A059413
Sequence in context: A064167 A175455 A185253 * A119073 A028559 A249639
Adjacent sequences: A192086 A192087 A192088 * A192090 A192091 A192092


KEYWORD

nonn


AUTHOR

Sergi Elizalde, Jun 23 2011


STATUS

approved



