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A261855
Number of compositions of n into distinct parts where each part i is marked with a word of length i over a quaternary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
2
9, 92, 1562, 3908, 14791, 50208, 540552, 987120, 3138143, 7862580, 23436690, 204455140, 349297653, 956040232, 2228084512, 5599922904, 13449425997, 116772809532, 182990434794, 483410072060, 1033025269277, 2455590595520, 5184309618676, 12755194552152
OFFSET
4,1
COMMENTS
Also number of matrices with four 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
a(n) = A261836(n,4).
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))(4):
seq(a(n), n=4..40);
CROSSREFS
Column k=4 of A261836.
Sequence in context: A007403 A015587 A024117 * A076456 A297580 A306475
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved