A210541 - OEIS

%I #11 Aug 07 2023 08:04:26

%S 1,1,1,1,2,4,8,16,33,73,177,467,1309,3813,11409,34999,110510,361194,

%T 1226930,4334048,15877297,60049447,233426007,929616461,3786970033,

%U 15777120457,67260334185,293617319221,1312868943154,6010792180952

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

%C Column 4 of A210545

%H R. H. Hardin, <a href="/A210541/b210541.txt">Table of n, a(n) for n = 1..210</a>

%H Rigoberto Flórez, José L. Ramírez, Fabio A. Velandia, and Diego Villamizar, <a href="https://arxiv.org/abs/2308.02059">Some Connections Between Restricted Dyck Paths, Polyominoes, and Non-Crossing Partitions</a>, arXiv:2308.02059 [math.CO], 2023. See Table 1 p. 13.

%F a(n) = 1 if n<=4 else sum{i=0..n-4}(binomial(n-4,i)*a(i)). Proved by _R. J. Mathar_ in the Sequence Fans Mailing List.

%e Some solutions for n=13

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

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

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

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

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

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

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

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

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

%K nonn

%O 1,5

%A _R. H. Hardin_, Mar 22 2012