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 A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards. 1

%I #7 Feb 12 2019 12:16:15

%S 1,2,5,15,39,104,281,771,2122,5858,16174,44694,123510,341403,943694,

%T 2608709,7211359,19935055,55108220,152341402,421132682,1164181573,

%U 3218268552,8896600238,24593808939,67987267220,187944382019,519554527901

%N Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A280064/b280064.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3) + 5*a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) for n>9.

%F Empirical g.f.: x*(1 + x)*(1 - 2*x + 4*x^3 - 8*x^4 + 2*x^5 - x^6 - x^7) / ((1 - x + x^2)*(1 - 2*x - 4*x^2 + 4*x^3 + 3*x^4 + x^5)). - _Colin Barker_, Feb 12 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A280069.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 25 2016

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Last modified October 3 10:50 EDT 2023. Contains 365861 sequences. (Running on oeis4.)