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A277563 Fifth column of Euler's difference table in A068106. 1
0, 0, 0, 24, 96, 504, 3216, 24024, 205056, 1965624, 20886576, 243511704, 3089233056, 42351635064, 623815221456, 9823096307544, 164655323578176, 2926840752827064, 54988308080981616, 1088680464831056664, 22653422225916839136, 494229434646381585144, 11280809162286897977616 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is 24 times the sequence A001909.

For n >= 5, this is the number of permutations that avoid substrings j(j+4), 1 <= j <= n-4.

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

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.

Enrique Navarrete, Forbidden Substrings in Circular K-Successions, arXiv:1702.02637 [math.CO], 2017.

FORMULA

For n>=5: a(n) = Sum_{j=0..n-4} (-1)^j*binomial(n-4,j)*(n-j)!.

a(n) ~ n!/e.

EXAMPLE

a(6) = 504 since there are 504 permutations in S6 that avoid the substrings {15,26}.

MATHEMATICA

Array[Sum[(-1)^j*Binomial[# - 4, j] (# - j)!, {j, 0, # - 4} ] &, 23] (* Michael De Vlieger, Dec 06 2016 *)

CROSSREFS

Cf. A001909, A068106.

Sequence in context: A183009 A272871 A319577 * A225790 A042122 A042124

Adjacent sequences:  A277560 A277561 A277562 * A277564 A277565 A277566

KEYWORD

nonn

AUTHOR

Enrique Navarrete, Dec 03 2016

STATUS

approved

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Last modified May 24 16:36 EDT 2022. Contains 354042 sequences. (Running on oeis4.)