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Number of nX2 0..1 arrays with every element equal to 1, 2 or 3 king-move adjacent elements, with upper left element zero.
5

%I #4 Jan 06 2018 10:54:14

%S 1,4,17,49,166,573,1933,6538,22165,75089,254350,861661,2919029,

%T 9888610,33499125,113483321,384441606,1302353053,4411914717,

%U 14946017274,50631856149,171522942625,581059476926,1968425392285,6668333757637

%N Number of nX2 0..1 arrays with every element equal to 1, 2 or 3 king-move adjacent elements, with upper left element zero.

%C Column 2 of A297823.

%H R. H. Hardin, <a href="/A297817/b297817.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A297823.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 06 2018