OFFSET
1,5
COMMENTS
For n >= 6, this is the number of permutations of [n] that avoid substrings j(j+5), 1 <= j <= n-5.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..400
Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.
FORMULA
For n>=6: a(n) = Sum_{j=0..n-5} (-1)^j*binomial(n-5,j)*(n-j)!.
Note a(n)/n! ~ 1/e.
EXAMPLE
a(9) = 229080 since there are 229080 permutations in S9 that avoid substrings {16,27,38,49}.
MATHEMATICA
a[1]=a[2]=a[3]=a[4]=0; a[5]=120; a[6]=600; a[n_]:=Sum[(-1)^j*Binomial[n-5, j]*(n-j)!, {j, 0, n-5}]; Table[a[n], {n, 1, 23}] (* Indranil Ghosh, Feb 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jan 02 2017
STATUS
approved