cp's OEIS Frontend

A210542 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times.

%I A210542 #16 Jul 22 2025 22:30:48
%S A210542 1,1,1,1,1,2,4,8,16,32,65,138,315,782,2090,5885,17112,50743,152705,
%T A210542 466760,1455562,4658963,15392116,52663709,186632887,683133153,
%U A210542 2570929570,9900731604,38864321047,155126476313,629028834312,2592051975917
%N A210542 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times.
%H A210542 R. H. Hardin, <a href="/A210542/b210542.txt">Table of n, a(n) for n = 1..210</a>
%H A210542 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 A210542 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 A210542 Some solutions for n=15:
%e A210542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210542 ..0....1....0....0....1....1....0....1....0....1....1....1....0....1....1....1
%e A210542 ..0....0....0....0....0....0....1....1....1....0....1....0....0....1....1....0
%e A210542 ..1....1....0....1....1....1....1....1....0....1....1....1....1....1....1....0
%e A210542 ..0....0....1....0....1....0....1....0....0....1....0....0....1....1....1....1
%e A210542 ..1....0....1....1....0....1....1....1....1....1....0....0....0....1....1....0
%e A210542 ..0....0....1....1....0....1....1....1....1....1....0....0....1....1....1....1
%e A210542 ..0....1....0....0....1....1....1....2....1....0....1....0....1....2....0....1
%e A210542 ..0....0....0....0....0....2....1....0....1....1....1....1....1....2....1....0
%e A210542 ..0....1....1....1....0....2....1....1....0....0....0....1....1....0....0....0
%e A210542 ..0....0....1....1....0....0....1....0....1....1....0....0....2....2....0....1
%Y A210542 Column 5 of A210545.
%K A210542 nonn
%O A210542 1,6
%A A210542 _R. H. Hardin_, Mar 22 2012