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Number of nX6 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
1

%I #4 Mar 25 2018 11:27:24

%S 13,14,26,45,99,254,696,2013,5953,17878,54126,164525,501455,1530694,

%T 4676360,14293737,43703389,133647942,408746766,1250182369,3823920719,

%U 11696450282,35777089740,109435800649,334746407201,1023938030574

%N Number of nX6 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

%C Column 6 of A301662.

%H R. H. Hardin, <a href="/A301660/b301660.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -14*a(n-4) -7*a(n-5) +3*a(n-6) +44*a(n-7) +22*a(n-8) -28*a(n-9) -45*a(n-10) -15*a(n-11) +25*a(n-12) +22*a(n-13) +2*a(n-14) -11*a(n-15) -4*a(n-16) +a(n-17) +2*a(n-18)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A301662.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 25 2018