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Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 6 times.
4

%I #9 Feb 02 2022 12:23:10

%S 1,1,1,1,1,1,2,4,8,16,32,64,129,267,582,1364,3454,9338,26429,76929,

%T 227579,680113,2050000,6242818,19284165,60754153,196341570,654012814,

%U 2251195713,8005274899,29325473071,110181281435,422565983725

%N Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 6 times.

%H R. H. Hardin, <a href="/A210543/b210543.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) = 1 if n<=6 else Sum_{i=0..n-6} (binomial(n-6,i)*a(i)).

%e Some solutions for n=17

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

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

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

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

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

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

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

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

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

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

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

%Y Column 6 of A210545.

%K nonn

%O 1,7

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