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Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
1

%I #4 Mar 11 2017 08:14:41

%S 5,282,4313,67892,945100,12699250,164714523,2089140956,26034179747,

%T 320066184088,3892257109768,46912556808052,561231923565665,

%U 6671995763846662,78889299491699749,928412437363667396

%N Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%C Column 5 of A283572.

%H R. H. Hardin, <a href="/A283569/b283569.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 26*a(n-1) -199*a(n-2) +132*a(n-3) +4265*a(n-4) -17778*a(n-5) -15431*a(n-6) +219544*a(n-7) -281138*a(n-8) -1030440*a(n-9) +2246322*a(n-10) +1755192*a(n-11) -1811285*a(n-12) -3285434*a(n-13) -13913513*a(n-14) +16913132*a(n-15) +1232775*a(n-16) +17203018*a(n-17) -24077179*a(n-18) -4811576*a(n-19) +3633696*a(n-20) +13901264*a(n-21) +3953216*a(n-22) -16310568*a(n-23) -2421451*a(n-24) +6596550*a(n-25) +5162315*a(n-26) -3560308*a(n-27) -4199693*a(n-28) +2503442*a(n-29) +1473667*a(n-30) -1059728*a(n-31) -255854*a(n-32) +261176*a(n-33) +18126*a(n-34) -39936*a(n-35) +1121*a(n-36) +3850*a(n-37) -347*a(n-38) -220*a(n-39) +29*a(n-40) +6*a(n-41) -a(n-42)

%e Some solutions for n=4

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

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

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

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

%Y Cf. A283572.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 11 2017