login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134515 Third column (k=2) of triangle A134832 (circular succession numbers). 2
1, 0, 0, 10, 15, 168, 1008, 8244, 73125, 726440, 7939008, 94744494, 1225760627, 17088219120, 255365758560, 4072255216296, 69021889788969, 1239055874931312, 23484788783212480, 468656477004105810, 9821896865573503095 (list; graph; refs; listen; history; text; internal format)
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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 14:21 EST 2018. Contains 318149 sequences. (Running on oeis4.)