A261842 - OEIS

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 #4 Sep 03 2015 05:14:44

%S 1,4,10,100,195,736,6032,11712,35285,100260,871386,1492820,4438573,

%T 10525720,29825140,241360728,405645867,1086289116,2489722574,

%U 6158961820,14573822743,123303661384,192326074572,504783599080,1073240557055,2539006453740,5337585654950

%N 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 Also matrices with four rows of nonnegative integers with distinct positive column sums and total element sum n.

%H Alois P. Heinz, <a href="/A261842/b261842.txt">Table of n, a(n) for n = 0..5000</a>

%p b:= proc(n, i, p) option remember;

%p `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+

%p `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+3, 3))))

%p end:

%p a:= n-> b(n$2, 0):

%p seq(a(n), n=0..40);

%Y Column k=4 of A261835.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 03 2015