login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277609 Fourth column of Euler's difference table in A068106. It is 6 times the sequence A000261. 4
0, 0, 6, 18, 78, 426, 2790, 21234, 183822, 1781802, 19104774, 224406930, 2864826126, 39486808938, 584328412518, 9238767895026, 155416555683150, 2771424197143914, 52216883883837702, 1036463580947218962, 21616958644969620174, 472612476001411964970, 10808196686285486012646 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For n >= 4, this is the number of permutations that avoid substrings j(j+3), 1 <= j <= n-3.
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
LINKS
Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.
Enrique Navarrete, Forbidden Substrings in Circular K-Successions, arXiv:1702.02637 [math.CO], 2017.
FORMULA
For n>=4: a(n) = Sum_{j=0..n-3} (-1)^j*binomial(n-3,j)*(n-j)!.
a(n) ~ exp(-1) * n!. - Vaclav Kotesovec, Oct 28 2016
EXAMPLE
a(5) = 78 since there are 78 permutations in S5 that avoid the substrings {14,25}.
MATHEMATICA
Table[Sum[(-1)^j*Binomial[n - 3, j] (n - j)!, {j, 0, n - 3}], {n, 23}] (* Michael De Vlieger, Oct 27 2016 *)
Flatten[{0, 0, Table[n!*Hypergeometric1F1[3-n, -n, -1], {n, 3, 20}]}] (* Vaclav Kotesovec, Oct 28 2016 *)
PROG
(PARI) a(n) = sum(j=0, n-3, (-1)^j*binomial(n-3, j)*(n-j)!); \\ Michel Marcus, Oct 29 2016
CROSSREFS
Sequence in context: A332939 A299412 A218080 * A188119 A239420 A219590
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Oct 23 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)