A192089 Number of permutations of [n] that require a 3-letter alphabet in order to be realized by a shift.
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
Offset: 2
Keywords
Examples
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
References
- S. Elizalde, The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765--786.
Links
- Sergi Elizalde, The number of permutations realized by a shift, arXiv:0909.2274v1 [math.CO]
Formula
a(n)=3^(n-2)+sum(psi_3(t)*3^(n-t-1),t=1..n-1)-n*sum(psi_2(t)*2^(n-t-1),t=0..n-1), where psi_N(t) is the number of primitive words of length t over an N-letter alphabet, which is expressible in terms of the Möbius function.
Comments