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Number of n X 4 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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`%I #9 Feb 14 2019 07:44:34
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`%S 11,338,10205,310365,9439606,287101721,8732086113,265582964074,
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`%T 8077601392565,245677069239189,7472171430204190,227263155064756577,
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`%U 6912119473224669225,210229395075140809474,6394044362928373953677
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`%N Number of n X 4 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
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`%H R. H. Hardin, <a href="/A280669/b280669.txt">Table of n, a(n) for n = 1..210</a>
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`%F Empirical: a(n) = 29*a(n-1) + 44*a(n-2) - 27*a(n-3) - 81*a(n-4) for n>5.
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`%F Empirical g.f.: x*(11 + 19*x - 81*x^2 - 155*x^3 + 18*x^4) / (1 - 29*x - 44*x^2 + 27*x^3 + 81*x^4). - _Colin Barker_, Feb 14 2019
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`%e Some solutions for n=3:
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`%e ..0..1..0..2. .0..0..1..1. .0..0..1..1. .0..1..2..2. .0..1..2..0
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`%e ..1..2..0..2. .2..0..2..1. .2..2..0..2. .2..0..0..2. .1..0..2..1
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`%e ..1..0..1..1. .1..0..0..1. .0..1..0..0. .1..1..0..2. .0..1..2..2
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`%Y Column 4 of A280673.
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`%K nonn
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`%O 1,1
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`%A _R. H. Hardin_, Jan 07 2017
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