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Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #6 May 19 2023 15:22:28

%S 1,46,996,16860,259040,3753846,52433492,713549156,9525564453,

%T 125290653912,1628677694816,20969760499276,267857168480060,

%U 3398651430782436,42877264217760487,538272025956290688

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

%C Column 3 of A280284.

%H R. H. Hardin, <a href="/A280280/b280280.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) -48*a(n-2) -636*a(n-3) +286*a(n-4) +4870*a(n-5) +2994*a(n-6) -7250*a(n-7) -20395*a(n-8) -27254*a(n-9) +18145*a(n-10) +42436*a(n-11) +25187*a(n-12) +8976*a(n-13) -53063*a(n-14) +3942*a(n-15) +11087*a(n-16) -3576*a(n-17) +616*a(n-18) -6944*a(n-19) -48*a(n-20) +512*a(n-21) -384*a(n-22) -256*a(n-24) for n>25.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A280284.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 30 2016