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Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times
1

%I #7 Aug 22 2012 12:04:29

%S 1,1,1,1,1,1,1,2,4,8,16,32,64,128,257,524,1106,2470,5924,15262,41690,

%T 118595,345861,1023028,3050590,9146312,27567958,83678750,256632743,

%U 798853376,2537255097,8264988956,27723246374,95941707086,342355797248

%N Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times

%C Column 7 of A210545

%H R. H. Hardin, <a href="/A210544/b210544.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) = 1 if n<=7 else sum{i=0..n-7}(binomial(n-7,i)*a(i))

%e Some solutions for n=19

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....1....1....0....1....1....0....1....1....1....1....0....1....0....0....0

%e ..1....1....0....0....0....1....1....0....0....1....1....1....0....1....1....1

%e ..1....0....1....1....1....0....1....0....0....1....0....0....0....1....0....1

%e ..0....1....0....0....0....1....1....0....1....1....1....1....0....1....1....1

%e ..0....0....1....0....1....0....1....0....1....0....1....0....0....1....1....0

%e ..1....0....0....1....1....1....0....0....0....1....1....0....1....1....1....0

%e ..0....1....1....0....1....1....0....0....0....1....1....1....0....1....1....0

%e ..0....1....1....0....1....1....0....0....1....0....1....0....0....1....1....1

%e ..1....1....1....1....0....1....0....0....1....1....2....1....1....0....1....0

%e ..1....1....1....1....0....2....0....0....0....1....1....1....1....0....2....1

%e ..0....0....1....1....1....1....0....0....1....0....1....1....0....1....2....1

%e ..0....1....1....1....0....2....1....1....1....0....0....0....1....1....2....1

%K nonn

%O 1,8

%A _R. H. Hardin_, formula proved by R. J. Mathar in the Sequence Fans Mailing List, Mar 22 2012