0,3

a(n) enumerates (ordered) lists of n 6-tuples such that every number from 1 to n appears once at each of the six tupel positions, and the j-th list member is not the tuple (j,j,j,j,j,j), for every j=1,..,n. Called coincidence-free 6-tuple lists of length n. See the Charalambides reference for this combinatorial interpretation.

Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 187, Exercise 13.(a), for r=6.

a(n)=sum(((-1)^(n-j))*binomial(n,j)*(j!)^6,j=0..n). See the Charalambides reference a(n)=B_{n,6}.

6-tuple combinatorics: a(1)=0 because the only list of 6-tupels composed of 1 is [(1,1,1,1,1,1)], and this is a coincidence for j=1.

6-tuple combinatorics: from the 2^6=64 possible 6-tupels of numbers 1 and 2 all exept (1,1,1,1,1,1) appear as first members of the length 2 lists. The second members are the 6-tuples obtained by interchanging 1 and 2 in the first member. E.g. one of the a(2)=2^6-1 =63 lists is [(1,1,1,1,1,2),(2,2,2,2,2,1)]. The list [(1,1,1,1,1,1),(2,2,2,2,2,2) does not qualify because it has in fact two coincidences, those for j=1 and j=2.

Cf. A135811 (coincidence-free 5-tuples). A135813 (coincidence-free 7-tuples).

Sequence in context: A001238 A110852 A136677 this_sequence A069452 A132591 A116232

Adjacent sequences: A135809 A135810 A135811 this_sequence A135813 A135814 A135815

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008