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Number of nX3 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #4 Feb 04 2017 09:14:09

%S 0,2,121,1054,7053,41118,226025,1189600,6090935,30538028,150719259,

%T 734621288,3544728240,16962264274,80602719361,380741691862,

%U 1789303173765,8371399843188,39012925707604,181180019619130,838816233474674

%N Number of nX3 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 3 of A281988.

%H R. H. Hardin, <a href="/A281983/b281983.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +5*a(n-2) -48*a(n-3) -41*a(n-4) +76*a(n-5) +53*a(n-6) -94*a(n-7) +35*a(n-8) +188*a(n-9) -90*a(n-10) -98*a(n-11) +106*a(n-12) +22*a(n-13) -182*a(n-14) +60*a(n-15) +8*a(n-16) -72*a(n-17) +12*a(n-18) -9*a(n-20) for n>23

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281988.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 04 2017