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Number of nX3 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #4 Jan 15 2017 07:36:16

%S 1,28,574,5590,48828,394202,3042893,22772368,166675727,1199580226,

%T 8520471567,59882031330,417204045166,2885615431576,19835570766874,

%U 135626535970070,923084270635629,6257223861792470,42263904928277217

%N Number of nX3 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 3 of A281129.

%H R. H. Hardin, <a href="/A281125/b281125.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) -70*a(n-3) -176*a(n-4) -366*a(n-5) -101*a(n-6) +541*a(n-7) +111*a(n-8) -731*a(n-9) -2114*a(n-10) -1900*a(n-11) +3502*a(n-12) +2900*a(n-13) -4597*a(n-14) -2319*a(n-15) +2436*a(n-16) +220*a(n-17) +76*a(n-18) +1492*a(n-19) +672*a(n-20) +160*a(n-21) +192*a(n-22) +64*a(n-23) for n>30

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281129.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 15 2017