A321956 Number of permutations of 3 indistinguishable copies of 1,...,n such that the first and second copies of j are adjacent and there are exactly j-1 numbers between the second and the third copy of j.

1, 1, 0, 2, 4, 0, 16, 40, 0, 456, 1759, 0, 34636, 175198, 0, 5494621, 34043062, 0

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Langford's Problem

Wikipedia, Dancing Links

Wikipedia, Langford pairing

Formula

a(n) = 0 for n == 2 (mod 3).

Example

a(3) = 2: 111332232, 332232111.
a(4) = 4: 111334432242, 332232441114, 334432242111, 441114332232.

Crossrefs

Cf. A264813, A322153.

Sequence in context: A059057 A196225 A127511 * A173315 A205975 A231915

Adjacent sequences: A321953 A321954 A321955 * A321957 A321958 A321959

Keyword

nonn,more

Author

Alois P. Heinz, Nov 22 2018

Status

approved