cp's OEIS Frontend

A261841 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.

%I A261841 #4 Sep 03 2015 04:29:56
%S A261841 1,3,6,46,75,231,1414,2376,5985,14151,89454,135330,343677,697017,
%T A261841 1657212,9439826,14381055,33119667,66361286,141451860,283907499,
%U A261841 1642516411,2346737106,5367877296,10093521943,20923900623,38428831710,80538197724,416229711735
%N A261841 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.
%C A261841 Also matrices with three rows of nonnegative integers with distinct positive column sums and total element sum n.
%H A261841 Alois P. Heinz, <a href="/A261841/b261841.txt">Table of n, a(n) for n = 0..5000</a>
%p A261841 b:= proc(n, i, p) option remember;
%p A261841       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p A261841       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+2, 2))))
%p A261841     end:
%p A261841 a:= n-> b(n$2, 0):
%p A261841 seq(a(n), n=0..40);
%Y A261841 Column k=3 of A261835.
%K A261841 nonn
%O A261841 0,2
%A A261841 _Alois P. Heinz_, Sep 03 2015