

A135812


Number of coincidencefree length n lists of 6tuples with all numbers 1,...,n in tuple position k, for k=1..6.


3




OFFSET

0,3


COMMENTS

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


REFERENCES

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..100


FORMULA

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


EXAMPLE

6tuple combinatorics: a(1)=0 because the only list of 6tuples composed of 1 is [(1,1,1,1,1,1)] and this is a coincidence for j=1.
6tuple combinatorics: from the 2^6=64 possible 6tuples of numbers 1 and 2 all except (1,1,1,1,1,1) appear as first members of the length 2 lists. The second members are the 6tuples obtained by interchanging 1 and 2 in the first member. E.g. one of the a(2)=2^61 =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.


MATHEMATICA

Table[Sum[(1)^(n  k)*Binomial[n, k]*(k!)^6, {k, 0, n}], {n, 0, 25}] (* G. C. Greubel, Nov 23 2016 *)


CROSSREFS

Cf. A135811 (coincidencefree 5tuples). A135813 (coincidencefree 7tuples).
Sequence in context: A212859 A239672 A136677 * A069452 A229846 A230674
Adjacent sequences: A135809 A135810 A135811 * A135813 A135814 A135815


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang Jan 21 2008


STATUS

approved



