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Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
1

%I #6 Jun 26 2022 05:16:57

%S 4,14,38,109,419,1413,4708,16406,56424,192997,664256,2285461,7852493,

%T 26999600,92853653,319251681,1097719967,3774663142,12979283717,

%U 44629543176,153461588223,527686255393,1814475510183,6239176643497

%N Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A317611.

%H R. H. Hardin, <a href="/A317606/b317606.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +5*a(n-2) +13*a(n-3) -22*a(n-4) -72*a(n-5) -88*a(n-6) +97*a(n-7) +314*a(n-8) +287*a(n-9) -138*a(n-10) -472*a(n-11) -290*a(n-12) +41*a(n-13) +93*a(n-14) -9*a(n-15) for n>17.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A317611.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 01 2018