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A243085 Number of compositions of n into parts with multiplicity not larger than 7.

%I A243085 #4 May 29 2014 16:58:45
%S A243085 1,1,2,4,8,16,32,64,127,255,502,1004,1972,3908,7660,15044,29361,57209,
%T A243085 110982,214648,413552,793936,1518344,2892496,5500825,10392649,
%U A243085 19569158,36845760,68891188,128241332,238736764,442162796,814790985,1499513369,2750419066
%N A243085 Number of compositions of n into parts with multiplicity not larger than 7.
%C A243085 Number of compositions of n avoiding the pattern {1}^8.
%H A243085 Alois P. Heinz, <a href="/A243085/b243085.txt">Table of n, a(n) for n = 0..1000</a>
%p A243085 b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p A243085       add(b(n-i*j, i-1, p+j)/j!, j=0..min(n/i, 7))))
%p A243085     end:
%p A243085 a:= n-> b(n$2, 0):
%p A243085 seq(a(n), n=0..50);
%Y A243085 Column k=7 of A243081.
%K A243085 nonn
%O A243085 0,3
%A A243085 _Alois P. Heinz_, May 29 2014