A320392 Number of permutations of 3 indistinguishable copies of 1,...,n such that there are exactly j numbers between the first and the third copy of j and floor(j/2) numbers between the first and the second or between the second and the third copy of j.

1, 1, 0, 0, 4, 4, 10, 24, 252, 410, 1998, 7798, 65188, 280582, 2281108, 10585748, 110903088

Offset

0,5

Comments

a(n) is even for n > 1.

Links

Table of n, a(n) for n=0..16.

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

Wikipedia, Dancing Links

Wikipedia, Langford pairing

Example

a(1) = 1: 111.
a(4) = 4: 111224234343, 111343432422, 224234343111, 343432422111.

Crossrefs

Cf. A285527, A322153.

Sequence in context: A219803 A320539 A145598 * A117881 A373101 A342989

Adjacent sequences: A320389 A320390 A320391 * A320393 A320394 A320395

Keyword

nonn,more

Author

Alois P. Heinz, Dec 06 2018

Status

approved