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

Author

Alois P. Heinz, Nov 25 2015

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Langford's Problem
• Wikipedia, Dancing Links
• Wikipedia, Langford pairing

Crossrefs

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