cp's OEIS Frontend

A210540 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times.

%I A210540 #18 Aug 07 2023 08:04:21
%S A210540 1,1,1,1,2,4,8,17,40,104,291,857,2634,8455,28424,100117,368465,
%T A210540 1410903,5599073,22968514,97267342,424927846,1913764155,8877181958,
%U A210540 42358589064,207639979365,1044360973987,5384167878948,28429186870051,153638182314504,849295001319211
%N A210540 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times.
%H A210540 Alois P. Heinz, <a href="/A210540/b210540.txt">Table of n, a(n) for n = 0..700</a> (terms n = 1..210 from R. H. Hardin)
%H A210540 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 A210540 a(n) = 1 if n<=3 else Sum_{i=0..n-3} binomial(n-3,i)*a(i). Proved by _R. J. Mathar_ in the Sequence Fans Mailing List.
%e A210540 Some solutions for n=11
%e A210540 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210540 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210540 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A210540 ..1....1....0....1....1....1....0....1....1....1....1....1....1....1....1....0
%e A210540 ..0....1....1....0....1....1....1....0....1....0....0....0....1....1....0....0
%e A210540 ..1....1....0....1....0....1....1....0....1....1....0....1....1....1....1....1
%e A210540 ..1....0....1....1....1....0....1....0....2....1....0....1....2....2....0....0
%e A210540 ..2....2....0....2....2....2....0....0....0....1....1....0....1....2....0....0
%e A210540 ..2....0....0....2....2....2....0....1....1....0....1....1....2....2....0....1
%e A210540 ..2....1....0....1....0....1....2....0....1....0....2....0....2....2....1....1
%e A210540 ..3....1....1....0....2....2....0....1....0....2....1....0....2....0....2....1
%Y A210540 Column 3 of A210545.
%K A210540 nonn
%O A210540 0,5
%A A210540 _R. H. Hardin_, Mar 22 2012
%E A210540 a(0)=1 prepended by _Alois P. Heinz_, Apr 24 2023