A261846 - OEIS

A261846

Number of compositions of n into distinct parts where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.

%I #4 Sep 03 2015 07:52:14

%S 1,8,36,696,2250,14712,245508,737352,3644355,17376832,325225824,

%T 823612736,3820113552,14264475648,66782014272,1254553664640,

%U 2949123559125,12008271483720,41150373332932,157262062899640,608878151760410,12804954311547288,27181470392583156

%N Number of compositions of n into distinct parts where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.

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

%H Alois P. Heinz, <a href="/A261846/b261846.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+7, 7))))

%p end:

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

%p seq(a(n), n=0..25);

%Y Column k=8 of A261835.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 03 2015