|
%I #30 Feb 23 2017 22:57:57
%S 0,0,0,24,96,504,3216,24024,205056,1965624,20886576,243511704,
%T 3089233056,42351635064,623815221456,9823096307544,164655323578176,
%U 2926840752827064,54988308080981616,1088680464831056664,22653422225916839136,494229434646381585144,11280809162286897977616
%N Fifth column of Euler's difference table in A068106.
%C This is 24 times the sequence A001909.
%C For n >= 5, this is the number of permutations that avoid substrings j(j+4), 1 <= j <= n-4.
%C For n>=5, the number of circular permutations (in cycle notation) on [n+1] that avoid substrings (j,j+5), 1<=j<=n-4. For example, for n=5, there are 96 circular permutations in S6 that avoid the substring {16}. Note that each of these circular permutations represent 6 permutations in one-line notation (see link 2017). - _Enrique Navarrete_, Feb 22 2017
%H Indranil Ghosh, <a href="/A277563/b277563.txt">Table of n, a(n) for n = 1..400</a>
%H Enrique Navarrete, <a href="http://arxiv.org/abs/1610.06217">Generalized K-Shift Forbidden Substrings in Permutations</a>, arXiv:1610.06217 [math.CO], 2016.
%H Enrique Navarrete, <a href="https://arxiv.org/abs/1702.02637">Forbidden Substrings in Circular K-Successions</a>, arXiv:1702.02637 [math.CO], 2017.
%F For n>=5: a(n) = Sum_{j=0..n-4} (-1)^j*binomial(n-4,j)*(n-j)!.
%F a(n) ~ n!/e.
%e a(6) = 504 since there are 504 permutations in S6 that avoid the substrings {15,26}.
%t Array[Sum[(-1)^j*Binomial[# - 4, j] (# - j)!, {j, 0, # - 4} ] &, 23] (* _Michael De Vlieger_, Dec 06 2016 *)
%Y Cf. A001909, A068106.
%K nonn
%O 1,4
%A _Enrique Navarrete_, Dec 03 2016
|
