|
|
A261857
|
|
Number of compositions of n into distinct parts where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
|
|
2
|
|
|
403, 3090, 26523, 178456, 4328268, 11655792, 55380132, 203857488, 908020203, 15089942326, 32659354659, 119798424120, 366557119686, 1229877368940, 4069268482608, 64750089252368, 122070519766665, 408439013722194, 1090232738714433, 3275624230408044
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
6,1
|
|
COMMENTS
|
Also number of matrices with six rows of nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to n and the column sums are distinct.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
`if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(6):
seq(a(n), n=6..30);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|