A264813 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 numbers between the second and the third copy of j.

1, 0, 1, 1, 0, 3, 6, 0, 53, 199, 0, 2908, 13699, 0, 369985, 2135430, 0, 87265700, 611286653, 0

Offset

0,6

Comments

a(n) = 0 for n == 1 (mod 3).

Links

Table of n, a(n) for n=0..19.

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

Wikipedia, Dancing Links

Wikipedia, Langford pairing

Example

a(0) = 1: the empty permutation.
a(2) = 1: 221121.
a(3) = 1: 223321131.
a(5) = 3: 223325534411514, 225523344531141, 552244253341131.
a(6) = 6: 221121665544336543, 225523366534411614, 225526633544361141, 446611415563322532, 552266253344631141, 665544336543221121.

Crossrefs

Cf. A014552, A104185, A108235, A176127, A203435, A261516, A261517, A321956.

Sequence in context: A299032 A094674 A125287 * A009014 A009036 A021281

Adjacent sequences: A264810 A264811 A264812 * A264814 A264815 A264816

Keyword

nonn,more

Author

Alois P. Heinz, Nov 25 2015

Status

approved