A261859 Number of compositions of n into distinct parts where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

2873, 66904, 4351388, 20331080, 157483354, 901563512, 6174438308, 180660353288, 511805155863, 2507827775824, 10089884785056, 44796664928048, 200977872433624, 5149800722642960, 11741438872834432, 48645418597510928, 159659060979170671, 593940633500376248

Offset

8,1

Comments

Also number of matrices with eight 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

Alois P. Heinz, Table of n, a(n) for n = 8..2000

Formula

a(n) = A261836(n,8).

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))(8):
seq(a(n), n=8..30);

Crossrefs

Column k=8 of A261836.

Sequence in context: A254587 A254580 A254355 * A286526 A081427 A101999

Adjacent sequences: A261856 A261857 A261858 * A261860 A261861 A261862

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved