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A277563
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Fifth column of Euler's difference table in A068106.
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1
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0, 0, 0, 24, 96, 504, 3216, 24024, 205056, 1965624, 20886576, 243511704, 3089233056, 42351635064, 623815221456, 9823096307544, 164655323578176, 2926840752827064, 54988308080981616, 1088680464831056664, 22653422225916839136, 494229434646381585144, 11280809162286897977616
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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For n>=5: a(n) = Sum_{j=0..n-4} (-1)^j*binomial(n-4,j)*(n-j)!.
a(n) ~ n!/e.
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EXAMPLE
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a(6) = 504 since there are 504 permutations in S6 that avoid the substrings {15,26}.
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MATHEMATICA
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Array[Sum[(-1)^j*Binomial[# - 4, j] (# - j)!, {j, 0, # - 4} ] &, 23] (* Michael De Vlieger, Dec 06 2016 *)
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CROSSREFS
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Cf. A001909, A068106.
Sequence in context: A183009 A272871 A319577 * A225790 A042122 A042124
Adjacent sequences: A277560 A277561 A277562 * A277564 A277565 A277566
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KEYWORD
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nonn
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AUTHOR
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Enrique Navarrete, Dec 03 2016
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STATUS
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approved
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