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

1,24

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

Table of n, a(n) for n=1..31.

Fausto A. C. Cariboni, Solutions for a(24)-a(25)

J. E. Miller, Langford's Problem.

Formula

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

Crossrefs

Cf. A014552, A059106, A059108, A261517.

Sequence in context: A198770 A222539 A219623 * A303608 A139610 A088404

Adjacent sequences: A284754 A284755 A284756 * A284758 A284759 A284760

Keyword

nonn,more

Author

Fausto A. C. Cariboni, Apr 02 2017

Extensions

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

Status

approved