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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. 2

%I #51 Mar 06 2024 04:46:49

%S 1,6,40,224,1152,5632,26624,122880,557056,2490368,11010048,48234496,

%T 209715200,905969664,3892314112,16642998272,70866960384,300647710720,

%U 1271310319616,5360119185408,22539988369408,94557999988736

%N 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 R. H. Hardin, <a href="/A229580/b229580.txt">Table of n, a(n) for n = 1..210</a>

%H 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 Empirical: a(n) = 8*a(n-1) - 16*a(n-2) for n>3.

%F a(n) = 4*a(n-1) + 4^(n-1) for n > 2. - _Gerald Hillier_, May 01 2018

%F a(n) = (2n - 1)*2^(2n - 3) for n > 1 [Gerson W. Barbosa]. - _Gerald Hillier_, May 02 2018

%F Empirical g.f.: x*(1 - 2*x + 8*x^2) / (1 - 4*x)^2. - _Colin Barker_, May 02 2018

%F a(n) = A002064(2n-2) - A002064(2n-3) for n > 1. - _Daniel Forgues_, Aug 31 2018

%F Empirical: a(n) = Integral_{t>0} dt/Beta(n-t,n+t) for n > 1. - _Gregory Gerard Wojnar_, Feb 10 2024

%e Some solutions for n=3:

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

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

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

%Y Column 2 of A229586.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 26 2013

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)