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Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Oct 12 2018 12:27:35

%S 8,97,732,5956,46516,368049,2908839,22987303,181744907,1436461093,

%T 11355392249,89758535679,709518658622,5608497091251,44333394421956,

%U 350441036671961,2770122870971545,21896924058038922,173088084934645189

%N Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 4 of A320402.

%H R. H. Hardin, <a href="/A320398/b320398.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +28*a(n-2) -24*a(n-3) -136*a(n-4) +105*a(n-5) -107*a(n-6) -286*a(n-7) -1000*a(n-8) +3256*a(n-9) -4082*a(n-10) +3419*a(n-11) -4880*a(n-12) +9893*a(n-13) +2718*a(n-14) +2078*a(n-15) +375*a(n-16) +9428*a(n-17) +6871*a(n-18) -13907*a(n-19) -47584*a(n-20) -33040*a(n-21) +3344*a(n-22) +35603*a(n-23) +39192*a(n-24) +3067*a(n-25) -15105*a(n-26) -15565*a(n-27) -3783*a(n-28) +6868*a(n-29) +3565*a(n-30) +414*a(n-31) -1909*a(n-32) -770*a(n-33) +339*a(n-34) +213*a(n-35) +64*a(n-36) -62*a(n-37) -13*a(n-38) +10*a(n-39) -a(n-40) for n>41

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A320402.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 12 2018