A210542 - OEIS

A210542

Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times

%I #14 Aug 07 2023 08:04:12

%S 1,1,1,1,1,2,4,8,16,32,65,138,315,782,2090,5885,17112,50743,152705,

%T 466760,1455562,4658963,15392116,52663709,186632887,683133153,

%U 2570929570,9900731604,38864321047,155126476313,629028834312,2592051975917

%N Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times

%H R. H. Hardin, <a href="/A210542/b210542.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 <= 5; otherwise, Sum_{i=0..n-5} binomial(n-5,i)*a(i). Proved by _R. J. Mathar_ in the Sequence Fans Mailing List.

%e Some solutions for n=15:

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

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

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

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

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

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

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

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

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

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

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

%Y Column 5 of A210545.

%K nonn

%O 1,6

%A _R. H. Hardin_, Mar 22 2012