|
| |
|
|
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, 7064747252076429464064, 105435171495207196553472, 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
|
|
|
|
FORMULA
|
|
|
|
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-François Alcover, Sep 29 2018, from formula in Assarpour et al. *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
a(28)-a(31) from Assarpour et al. (2015), added by Max Alekseyev, Sep 24 2023
|
|
|
STATUS
|
approved
|
| |
|
|
