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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 and with new values introduced in order 0 sequentially upwards.
1

%I #7 Dec 31 2023 16:15:24

%S 4,50,571,6727,78800,924579,10844773,127214104,1492251709,17504551617,

%T 205333329586,2408618523801,28253780677867,331424891961162,

%U 3887708335839063,45603925604339175,534947030615649624

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

%C Column 3 of A280362.

%H R. H. Hardin, <a href="/A280358/b280358.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) +26*a(n-2) -58*a(n-3) -99*a(n-4) -63*a(n-5) -25*a(n-6) +229*a(n-7) -3*a(n-8) -16*a(n-9) +12*a(n-10) +16*a(n-12).

%e Some solutions for n=4

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

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

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

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

%Y Cf. A280362.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2017