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Number of 3Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.
1

%I #6 Feb 13 2018 13:46:13

%S 1,3,14,26,43,109,301,649,1332,3124,7545,16925,37301,85611,198538,

%T 450262,1014883,2315761,5303161,12062833,27380904,62381096,142295761,

%U 323928537,736878729,1678132851,3823284742,8705263890,19816325051,45124192277

%N Number of 3Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.

%C Row 3 of A297431.

%H R. H. Hardin, <a href="/A297433/b297433.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +3*a(n-3) +8*a(n-4) +a(n-5) -a(n-6).

%F Empirical: G.f.: -x*(-1-2*x-11*x^2-9*x^3+x^5)/(1-x-3*x^3-8*x^4-x^5+x^6) . - _R. J. Mathar_, Feb 13 2018

%e Some solutions for n=5

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

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

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

%Y Cf. A297431.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 30 2017