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.

1, 6, 40, 224, 1152, 5632, 26624, 122880, 557056, 2490368, 11010048, 48234496, 209715200, 905969664, 3892314112, 16642998272, 70866960384, 300647710720, 1271310319616, 5360119185408, 22539988369408, 94557999988736

Offset: 1

Author

R. H. Hardin, Sep 26 2013

Keywords

• nonn

Examples

			Some solutions for n=3:
  0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 1   0 0
  0 0   2 0   0 1   0 2   1 0   2 2   1 2   2 1   0 2   1 2
  1 0   0 2   1 2   1 1   2 1   1 0   0 1   0 0   0 0   0 2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Matthew Blair, Rigoberto Flórez, and Antara Mukherjee, Honeycombs in the Pascal triangle and beyond, arXiv:2203.13205 [math.HO], 2022.

Crossrefs

Column 2 of A229586.

Formula

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

a(n) = 4*a(n-1) + 4^(n-1) for n > 2. - Gerald Hillier, May 01 2018

a(n) = (2n - 1)*2^(2n - 3) for n > 1 [Gerson W. Barbosa]. - Gerald Hillier, May 02 2018

Empirical g.f.: x*(1 - 2*x + 8*x^2) / (1 - 4*x)^2. - Colin Barker, May 02 2018

a(n) = A002064(2n-2) - A002064(2n-3) for n > 1. - Daniel Forgues, Aug 31 2018

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