A059108 - OEIS

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

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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