cp's OEIS Frontend

A261842 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.

%I A261842 #4 Sep 03 2015 05:14:44
%S A261842 1,4,10,100,195,736,6032,11712,35285,100260,871386,1492820,4438573,
%T A261842 10525720,29825140,241360728,405645867,1086289116,2489722574,
%U A261842 6158961820,14573822743,123303661384,192326074572,504783599080,1073240557055,2539006453740,5337585654950
%N A261842 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.
%C A261842 Also matrices with four rows of nonnegative integers with distinct positive column sums and total element sum n.
%H A261842 Alois P. Heinz, <a href="/A261842/b261842.txt">Table of n, a(n) for n = 0..5000</a>
%p A261842 b:= proc(n, i, p) option remember;
%p A261842       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p A261842       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+3, 3))))
%p A261842     end:
%p A261842 a:= n-> b(n$2, 0):
%p A261842 seq(a(n), n=0..40);
%Y A261842 Column k=4 of A261835.
%K A261842 nonn
%O A261842 0,2
%A A261842 _Alois P. Heinz_, Sep 03 2015