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%I #8 Apr 26 2024 19:25:34
%S 32,796,12771,266425,5297294,104126212,2073090293,41113855962,
%T 815396431544,16180271550797,320994645608890,6368309327679546,
%U 126345207041984379,2506615691847812429,49729959598966238800
%N Number of n X 5 0..1 arrays with no 1 equal to more than three of its king-move neighbors.
%C Column 5 of A282399.
%H R. H. Hardin, <a href="/A282396/b282396.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) +67*a(n-2) +1083*a(n-3) -2426*a(n-4) +10515*a(n-5) -140500*a(n-6) +51934*a(n-7) -1836687*a(n-8) +1800044*a(n-9) -6304076*a(n-10) +38948928*a(n-11) +41798022*a(n-12) +196747797*a(n-13) +12123969*a(n-14) -380890083*a(n-15) -1084561595*a(n-16) -192909953*a(n-17) +304349466*a(n-18) +6137798*a(n-19) +595433110*a(n-20) +4756579373*a(n-21) +6695241521*a(n-22) -4963971102*a(n-23) -14223342318*a(n-24) -5623266067*a(n-25) +12080079611*a(n-26) +7637732511*a(n-27) +1921641312*a(n-28) -5380530060*a(n-29) -7158323520*a(n-30) -2391797229*a(n-31) +2175504272*a(n-32) +4051021686*a(n-33) +2292601540*a(n-34) -1608641468*a(n-35) -548773830*a(n-36) +1492521963*a(n-37) -315357317*a(n-38) -16551126*a(n-39) +58658148*a(n-40) -15582344*a(n-41) -2137284*a(n-42) +649072*a(n-43) +65024*a(n-44).
%F Empirical formula confirmed. - _Robert Israel_, Apr 26 2024
%e Some solutions for n=3
%e ..0..0..0..1..0. .0..1..0..1..0. .1..1..1..0..0. .0..0..0..0..0
%e ..1..1..0..0..0. .1..0..0..0..1. .1..0..0..0..1. .1..1..1..0..1
%e ..1..0..0..1..0. .0..1..1..0..1. .0..0..1..0..1. .1..0..0..0..0
%Y Cf. A282399.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2017
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