A134515 Third column (k=2) of triangle A134832 (circular succession numbers).

1, 0, 0, 10, 15, 168, 1008, 8244, 73125, 726440, 7939008, 94744494, 1225760627, 17088219120, 255365758560, 4072255216296, 69021889788969, 1239055874931312, 23484788783212480, 468656477004105810, 9821896865573503095

Offset

0,4

Comments

a(n) enumerates circular permutations of {1,2,...,n+2} with exactly two successor pairs (i,i+1). Due to cyclicity also (n+2,1) is a successor pair.

References

Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 183, eq. (5.15), for k=2.

Links

Table of n, a(n) for n=0..20.

Bhadrachalam Chitturi and Krishnaveni K S, Adjacencies in Permutations, arXiv preprint arXiv:1601.04469 [cs.DM], 2016.

Formula

E.g.f.: (d^2/dx^2) (x^2/2!)*(1-log(1-x))/e^x.

a(n) = (((n+2)*(n+1))/2)*A000757(n), n>=0.

Example

a(2)=0 because the 4!/4 = 6 circular permutations of n=4 elements (1,2,3,4), (1,4,3,2), (1,3,4,2),(1,2,4,3), (1,4,2,3) and (1,3,2,4) have 4,0,1,1,1 and 1 successor pair, respectively.

Crossrefs

Cf. A135799 (column k=1).

Sequence in context: A238759 A278349 A114703 * A232608 A175335 A167788

Adjacent sequences: A134512 A134513 A134514 * A134516 A134517 A134518

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 21 2008, Feb 22 2008

Status

approved