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A180189 Number of permutations of [n] having exactly 1 circular succession. A circular succession in a permutation p of [n] is either a pair p(i), p(i+1), where p(i+1)=p(i)+1 or the pair p(n), p(1) if p(1)=p(n)+1. 3
0, 2, 0, 12, 40, 270, 1848, 14840, 133488, 1334970, 14684560, 176214852, 2290792920, 32071101062, 481066515720, 7697064251760, 130850092279648, 2355301661033970, 44750731559645088, 895014631192902140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For example, p=(4,1,2,5,3) has 2 circular successions: (1,2) and (3,4).

a(n)=A180188(n,1).

REFERENCES

S. M. Tanny, Permutations and successions, J. Combinatorial Theory, Series A, 21 (1976), 196-202.

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n)=n(n-1)d(n-2), where d(j)=A000166(j) are the derangement numbers.

EXAMPLE

a(4)=12 because we have 1*243, 142*3, 13*42, 31*24, 3142*, 431*2, 213*4, 4213*, 2*314, 2431*, 42*31, and 3*421 (the circular succession is marked *).

MAPLE

d[0] := 1: for n to 51 do d[n] := n*d[n-1]+(-1)^n end do: seq(n*(n-1)*d[n-2], n = 1 .. 22);

CROSSREFS

Cf. A000166, A180188

Sequence in context: A134831 A074001 A228621 * A182437 A013316 A013310

Adjacent sequences:  A180186 A180187 A180188 * A180190 A180191 A180192

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Sep 06 2010

STATUS

approved

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Last modified May 26 22:16 EDT 2019. Contains 323597 sequences. (Running on oeis4.)