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%I A210544 #9 Jul 07 2025 19:30:17
%S A210544 1,1,1,1,1,1,1,2,4,8,16,32,64,128,257,524,1106,2470,5924,15262,41690,
%T A210544 118595,345861,1023028,3050590,9146312,27567958,83678750,256632743,
%U A210544 798853376,2537255097,8264988956,27723246374,95941707086,342355797248
%N A210544 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times.
%C A210544 Column 7 of A210545.
%H A210544 R. H. Hardin, <a href="/A210544/b210544.txt">Table of n, a(n) for n = 1..210</a>
%F A210544 a(n) = 1 if n<=7 else Sum_{i=0..n-7} binomial(n-7,i)*a(i).
%e A210544 Some solutions for n=19
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210544 ..0....1....1....0....1....1....0....1....1....1....1....0....1....0....0....0
%e A210544 ..1....1....0....0....0....1....1....0....0....1....1....1....0....1....1....1
%e A210544 ..1....0....1....1....1....0....1....0....0....1....0....0....0....1....0....1
%e A210544 ..0....1....0....0....0....1....1....0....1....1....1....1....0....1....1....1
%e A210544 ..0....0....1....0....1....0....1....0....1....0....1....0....0....1....1....0
%e A210544 ..1....0....0....1....1....1....0....0....0....1....1....0....1....1....1....0
%e A210544 ..0....1....1....0....1....1....0....0....0....1....1....1....0....1....1....0
%e A210544 ..0....1....1....0....1....1....0....0....1....0....1....0....0....1....1....1
%e A210544 ..1....1....1....1....0....1....0....0....1....1....2....1....1....0....1....0
%e A210544 ..1....1....1....1....0....2....0....0....0....1....1....1....1....0....2....1
%e A210544 ..0....0....1....1....1....1....0....0....1....0....1....1....0....1....2....1
%e A210544 ..0....1....1....1....0....2....1....1....1....0....0....0....1....1....2....1
%Y A210544 Cf. A210545.
%K A210544 nonn
%O A210544 1,8
%A A210544 _R. H. Hardin_, formula proved by _R. J. Mathar_ in the Sequence Fans Mailing List, Mar 22 2012