A261854 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a ternary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

7, 21, 96, 832, 1539, 4281, 10902, 76020, 117585, 306639, 634686, 1537206, 9013319, 13793487, 32005392, 64458596, 138068775, 278292429, 1622912266, 2321086080, 5318890971, 10014128239, 20784037248, 38209197732, 80154402633, 415073903937, 593664848658

Offset

3,1

Comments

Also number of matrices with three 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 = 3..2500

Formula

a(n) = A261836(n,3):

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))(3):
seq(a(n), n=3..40);

Crossrefs

Column k=3 of A261836.

Sequence in context: A121157 A347863 A253072 * A219152 A038184 A001185

Adjacent sequences: A261851 A261852 A261853 * A261855 A261856 A261857

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved