login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004075 Number of Skolem sequences of order n. 8
1, 0, 0, 6, 10, 0, 0, 504, 2656, 0, 0, 455936, 3040560, 0, 0, 1400156768, 12248982496, 0, 0, 11435578798976, 123564928167168, 0, 0, 204776117691241344, 2634563519776965376, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Number of permutations of the multiset {1,1,2,2,...,n,n} such that the distance between the elements i equals i for every i=1,2,...,n.

Number of super perfect rhythmic tilings of [0,2n-1] with pairs. See A285698 and A285527 for the definition and tilings of triples and quadruples. - Tony Reix, Apr 25 2017

REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 460.

LINKS

Table of n, a(n) for n=1..27.

Ali Assarpour, Amotz Bar-Noy, Ou Liuo, Counting the Number of Langford Skolem Pairings, arXiv:1507.00315 [cs.DM], 2015.

S. Burrill and L. Yen, Constructing Skolem sequences via generating trees, arXiv preprint arXiv:1301.6424 [math.CO], 2013.

J. E. Miller, Langford's Problem

G. Nordh, Perfect Skolem sequences, arXiv:math/0506155 [math.CO], 2005.

FORMULA

For n>1, a(n)=A059106(n)*2 because A059106 ignores reflected solutions. - Martin Fuller, Mar 08 2007

MATHEMATICA

(* Program not suitable to compute a large number of terms. *)

iter[n_] := Sequence @@ Table[{x[i], {-1, 1}}, {i, 1, 2n}];

a[n_] := 1/2^(2n) Sum[Product[x[i], {i, 1, 2n}] Product[Sum[x[k] x[k+i], {k, 1, 2n-i}], {i, 1, n}], iter[n] // Evaluate];

Table[Print[a[n]]; a[n], {n, 1, 10}] (* Jean-Fran├žois Alcover, Sep 29 2018, from formula in Assarpour et al. *)

CROSSREFS

Cf. A014552, A059106, A176127, A268537.

Sequence in context: A110460 A159190 A236766 * A202951 A316633 A295052

Adjacent sequences:  A004072 A004073 A004074 * A004076 A004077 A004078

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms (via A059106) from Martin Fuller, Mar 08 2007

Extended using results from the Assarpour et al. (2015) paper by N. J. A. Sloane, Feb 22 2016 at the suggestion of William Rex Marshall

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 September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)