A125762 Number of planar Langford sequences.

0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 16, 40, 0, 0, 194, 274, 0, 0, 2384, 4719, 0, 0, 31856, 62124, 0, 0, 426502, 817717, 0, 0, 5724640, 10838471, 0, 0, 75178742, 142349245, 0, 0, 977964587, 1850941916, 0, 0

Offset

1,8

Comments

Enumerates the Langford sequences (counted by A014552) that have the additional property that we can draw noncrossing lines to connect the two 1s, the two 2s, ..., the two ns. For example, the four solutions for n=8 are 8642752468357131, 8613175368425724, 5286235743681417, 7528623574368141.

References

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

Links

Table of n, a(n) for n=1..42.

John E. Miller, Langford's Problem

Edward Moody, Java program for enumerating planar Langford sequences

Zan Pan, Conjectures on the number of Langford sequences, (2021).

Crossrefs

Cf. A014552, A059106.

Sequence in context: A028699 A019259 A019218 * A286216 A280727 A232357

Adjacent sequences: A125759 A125760 A125761 * A125763 A125764 A125765

Keyword

nonn,more

Author

Don Knuth, Feb 03 2007

Extensions

a(31) from Rory Molinari, Feb 21 2018

a(32)-a(34) from Rory Molinari, Mar 10 2018

a(35) from Rory Molinari, May 02 2018

a(36)-a(42) from Edward Moody, Apr 02 2019

Status

approved