A059108 Number of solutions to variant of triples version of Langford (or Langford-Skolem) problem.

1, 1, 0, 0, 0, 0, 0, 0, 0, 9, 20, 33, 0, 0, 0, 0, 0, 0, 200343, 869006, 4247790, 0, 0, 0, 0, 0, 0

Offset

0,10

Comments

How many ways are of arranging the numbers 1,1,1,2,2,2,3,3,3,...,n,n,n so that there are zero numbers between the first and second 1's and zero numbers between the second and third 1's; one number between the first and second 2's and one number between the second and third 2's; ... n-1 numbers between the first and second n's and n-1 numbers between the second and third n's?

a(n)=0 for n mod 9 not in {0,1,2}. - Gheorghe Coserea, Aug 23 2017

Links

Table of n, a(n) for n=0..26.

Gheorghe Coserea, Solutions for n=10.

Gheorghe Coserea, Solutions for n=11.

J. E. Miller, Langford's Problem

Example

From Gheorghe Coserea, Jul 14 2017: (Start)
For n=9 the a(9)=9 solutions, up to reversal of the order, are:
2 4 2 8 2 4 6 7 9 4 3 8 6 3 7 5 3 9 6 8 5 7 1 1 1 5 9
2 4 2 9 2 4 5 6 7 4 8 5 9 6 3 7 5 3 8 6 3 9 7 1 1 1 8
4 2 5 2 4 2 9 5 4 7 8 3 5 6 3 9 7 3 8 6 1 1 1 7 9 6 8
5 1 1 1 7 5 8 6 9 3 5 7 3 6 8 3 4 9 7 6 4 2 8 2 4 2 9
5 6 1 1 1 5 8 6 9 3 5 7 3 6 8 3 4 9 7 2 4 2 8 2 4 7 9
6 7 9 2 5 2 6 2 7 5 8 9 6 3 5 7 3 4 8 3 9 4 1 1 1 4 8
6 7 9 2 5 2 6 2 7 5 8 9 6 4 5 7 3 4 8 3 9 4 3 1 1 1 8
7 4 2 8 2 4 2 7 9 4 3 8 6 3 7 5 3 9 6 8 5 1 1 1 6 5 9
7 5 3 6 9 3 5 7 3 6 8 5 4 9 7 6 4 2 8 2 4 2 9 1 1 1 8
(End)

Crossrefs

Cf. A014552, A050998, A059106, A059107.

Sequence in context: A256383 A322433 A017497 * A028566 A147479 A146680

Adjacent sequences: A059105 A059106 A059107 * A059109 A059110 A059111

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane, Feb 14 2001

Extensions

Fausto A. C. Cariboni has confirmed the values a(1) to a(20). - N. J. A. Sloane, Mar 27 2017

a(21) from Fausto A. C. Cariboni, Mar 28 2017

Status

approved