A284757 Number of solutions to Nickerson variant of quadruples version of Langford (or Langford-Skolem) problem.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 55, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Fausto A. C. Cariboni, Apr 02 2017

Keywords

• nonn
• more

Comments

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

An equivalent definition is A261517 with added condition that all different common intervals are <= n.

a(n) ignores reflected solutions.

Links

• Fausto A. C. Cariboni, Solutions for a(24)-a(25)
• J. E. Miller, Langford's Problem.

Crossrefs

Cf. A014552, A059106, A059108, A261517.

Formula

a(n) = 0 if (n mod 8) not in {0, 1}. - Max Alekseyev, Sep 28 2023

Extensions

a(28)-a(31) from Max Alekseyev, Sep 24 2023