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 A059108 Number of solutions to variant of triples version of Langford (or Langford-Skolem) problem. 8
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 13:23 EDT 2024. Contains 375938 sequences. (Running on oeis4.)