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%I #23 Sep 28 2023 12:11:23
%S 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
%N Number of solutions to Nickerson variant of quadruples version of Langford (or Langford-Skolem) problem.
%C 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?
%C An equivalent definition is A261517 with added condition that all different common intervals are <= n.
%C a(n) ignores reflected solutions.
%H Fausto A. C. Cariboni, <a href="/A284757/a284757.txt">Solutions for a(24)-a(25)</a>
%H J. E. Miller, <a href="http://dialectrix.com/langford.html">Langford's Problem</a>.
%F a(n) = 0 if (n mod 8) not in {0, 1}. - _Max Alekseyev_, Sep 28 2023
%Y Cf. A014552, A059106, A059108, A261517.
%K nonn,more
%O 1,24
%A _Fausto A. C. Cariboni_, Apr 02 2017
%E a(28)-a(31) from _Max Alekseyev_, Sep 24 2023
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