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A229681 Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order. 1

%I

%S 0,360,10896,186576,2700432,35485776,437924880,5169543120,59031049104,

%T 656886585168,7159989801744,76729919248080,810700618461840,

%U 8463178886657616,87441690785378832,895373932606109136

%N Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%C Column 4 of A229685.

%H R. H. Hardin, <a href="/A229681/b229681.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*a(n-1) -243*a(n-2) +729*a(n-3) for n>6.

%F Conjectures from _Colin Barker_, Jun 16 2017: (Start)

%F G.f.: 24*x^2*(15 + 49*x - 839*x^2 + 2007*x^3 - 1296*x^4) / (1 - 9*x)^3.

%F a(n) = 16*3^(2*n-7)*(-449 + 60*n + 256*n^2) for n>3.

%F (End)

%e Some solutions for n=3

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Sep 27 2013

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Last modified September 29 20:22 EDT 2020. Contains 337432 sequences. (Running on oeis4.)