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A279575 Number of n X 3 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 1

%I

%S 2,36,944,23072,547168,12701248,290067328,6540226304,145949741056,

%T 3229393518592,70948621604864,1549301789257728,33656105642434560,

%U 727817498719862784,15676632552910815232,336475872266838999040

%N Number of n X 3 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279575/b279575.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 44*a(n-1) - 556*a(n-2) + 1616*a(n-3) - 2000*a(n-4) + 1152*a(n-5) - 256*a(n-6) for n>7.

%F Empirical g.f.: 2*x*(1 - 2*x)^2*(1 - 22*x + 144*x^2 - 176*x^3 + 64*x^4) / (1 - 22*x + 36*x^2 - 16*x^3)^2. - _Colin Barker_, Feb 11 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A279580.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 15 2016

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Last modified January 23 06:38 EST 2022. Contains 350504 sequences. (Running on oeis4.)