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Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Mar 02 2018 17:55:36

%S 4,13,20,45,148,529,1747,5797,19584,66222,223320,753486,2543959,

%T 8589093,28995289,97886648,330471005,1115681398,3766562359,

%U 12716019134,42929679141,144931880115,489294288989,1651872133532,5576769838008

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A300314.

%H R. H. Hardin, <a href="/A300309/b300309.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -6*a(n-2) +6*a(n-3) -16*a(n-4) +3*a(n-5) -3*a(n-6) +41*a(n-7) -21*a(n-9) +14*a(n-10) -66*a(n-11) +43*a(n-12) -46*a(n-13) +41*a(n-14) -8*a(n-15) +20*a(n-16) for n>17

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300314.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2018