A304271 Number of unrestricted planar Langford sequences.

0, 0, 1, 1, 0, 0, 6, 24, 0, 0, 139, 289, 0, 0, 2414, 4455, 0, 0, 33222, 63700, 0, 0, 437489, 794953, 0, 0

Offset

1,7

Comments

Enumerates the Langford sequences (counted by A014552) that are planar in a sense more general than the one used by A125762. In that sequence the noncrossing joining lines are each restricted to lie in one of the two half-planes separated by the axis of the numerical sequence. Here we allow the joining lines to use the whole plane, requiring them only to be noncrossing and not to pass between the terms of the Langford sequence.

References

D. E. Knuth, TAOCP, Vol. 4, in preparation.

Links

Table of n, a(n) for n=1..26.

John E. Miller, Langford's Problem

Example

When n=4 the Langford sequence 23421314 is not planar in the sense of A125762, but is planar in the sense of this sequence: the line that joins the 3s does not lie entirely "above" or "below" the numerical array but passes around the end of the array.

Crossrefs

Cf. A014552, A125762.

Sequence in context: A154420 A255305 A339628 * A293590 A194770 A052697

Adjacent sequences: A304268 A304269 A304270 * A304272 A304273 A304274

Keyword

nonn,more

Author

Rory Molinari, May 09 2018

Extensions

a(23) from Rory Molinari, Jun 04 2019

a(24)-a(26) from Rory Molinari, Dec 02 2019

Status

approved