cp's OEIS Frontend

A277609 Fourth column of Euler's difference table in A068106. It is 6 times the sequence A000261.

%I A277609 #45 Feb 23 2017 22:58:33
%S A277609 0,0,6,18,78,426,2790,21234,183822,1781802,19104774,224406930,
%T A277609 2864826126,39486808938,584328412518,9238767895026,155416555683150,
%U A277609 2771424197143914,52216883883837702,1036463580947218962,21616958644969620174,472612476001411964970,10808196686285486012646
%N A277609 Fourth column of Euler's difference table in A068106. It is 6 times the sequence A000261.
%C A277609 For n >= 4, this is the number of permutations that avoid substrings j(j+3), 1 <= j <= n-3.
%C A277609 For n>=4, the number of circular permutations (in cycle notation) on [n+1] that avoid substrings (j,j+4), 1<=j<=n-3.  For example, for n=4, there are 18 circular permutations in S5 that avoid the substring {15}. Note that each of these circular permutations represent 5 permutations in one-line notation (see link 2017). - _Enrique Navarrete_, Feb 22 2017
%H A277609 Indranil Ghosh, <a href="/A277609/b277609.txt">Table of n, a(n) for n = 1..400</a>
%H A277609 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 A277609 Enrique Navarrete, <a href="https://arxiv.org/abs/1702.02637">Forbidden Substrings in Circular K-Successions</a>, arXiv:1702.02637 [math.CO], 2017.
%F A277609 For n>=4: a(n) = Sum_{j=0..n-3} (-1)^j*binomial(n-3,j)*(n-j)!.
%F A277609 a(n) ~ exp(-1) * n!. - _Vaclav Kotesovec_, Oct 28 2016
%e A277609 a(5) = 78 since there are 78 permutations in S5 that avoid the substrings {14,25}.
%t A277609 Table[Sum[(-1)^j*Binomial[n - 3, j] (n - j)!, {j, 0, n - 3}], {n, 23}] (* _Michael De Vlieger_, Oct 27 2016 *)
%t A277609 Flatten[{0, 0, Table[n!*Hypergeometric1F1[3-n, -n, -1], {n, 3, 20}]}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o A277609 (PARI) a(n) = sum(j=0, n-3, (-1)^j*binomial(n-3,j)*(n-j)!); \\ _Michel Marcus_, Oct 29 2016
%Y A277609 Cf. A068106, A000261.
%K A277609 nonn
%O A277609 1,3
%A A277609 _Enrique Navarrete_, Oct 23 2016