A261854 - OEIS

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

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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