cp's OEIS Frontend

A229580 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%I A229580 #51 Mar 06 2024 04:46:49
%S A229580 1,6,40,224,1152,5632,26624,122880,557056,2490368,11010048,48234496,
%T A229580 209715200,905969664,3892314112,16642998272,70866960384,300647710720,
%U A229580 1271310319616,5360119185408,22539988369408,94557999988736
%N A229580 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%H A229580 R. H. Hardin, <a href="/A229580/b229580.txt">Table of n, a(n) for n = 1..210</a>
%H A229580 Matthew Blair, Rigoberto Flórez, and Antara Mukherjee, <a href="https://arxiv.org/abs/2203.13205">Honeycombs in the Pascal triangle and beyond</a>, arXiv:2203.13205 [math.HO], 2022.
%F A229580 Empirical: a(n) = 8*a(n-1) - 16*a(n-2) for n>3.
%F A229580 a(n) = 4*a(n-1) + 4^(n-1) for n > 2. - _Gerald Hillier_, May 01 2018
%F A229580 a(n) = (2n - 1)*2^(2n - 3) for n > 1 [Gerson W. Barbosa]. - _Gerald Hillier_, May 02 2018
%F A229580 Empirical g.f.: x*(1 - 2*x + 8*x^2) / (1 - 4*x)^2. - _Colin Barker_, May 02 2018
%F A229580 a(n) = A002064(2n-2) - A002064(2n-3) for n > 1. - _Daniel Forgues_, Aug 31 2018
%F A229580 Empirical: a(n) = Integral_{t>0} dt/Beta(n-t,n+t) for n > 1. - _Gregory Gerard Wojnar_, Feb 10 2024
%e A229580 Some solutions for n=3:
%e A229580   0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 0
%e A229580   0 0   2 0   0 1   0 2   1 0   2 2   1 2   2 1   0 2   1 2
%e A229580   1 0   0 2   1 2   1 1   2 1   1 0   0 1   0 0   0 0   0 2
%Y A229580 Column 2 of A229586.
%K A229580 nonn
%O A229580 1,2
%A A229580 _R. H. Hardin_, Sep 26 2013