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%I #4 Feb 14 2014 07:14:08
%S 21,325,3373,31651,315896,3255233,33328972,338653847,3440498469,
%T 35005538562,356277110111,3625220129423,36883657486461,
%U 375271668222454,3818293078009309,38850130701960925,395287712822929199
%N Number of (n+1)X(5+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors
%C Column 5 of A237859
%H R. H. Hardin, <a href="/A237856/b237856.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -55*a(n-2) +260*a(n-3) +106*a(n-4) -712*a(n-5) +4133*a(n-6) +3199*a(n-7) -66365*a(n-8) -62986*a(n-9) +204948*a(n-10) +398282*a(n-11) +180607*a(n-12) -153036*a(n-13) -2057833*a(n-14) -3455014*a(n-15) +2273843*a(n-16) +9053828*a(n-17) +2595573*a(n-18) -8330986*a(n-19) -4084846*a(n-20) +1955600*a(n-21) -2056080*a(n-22) +508497*a(n-23) +6091834*a(n-24) +1292602*a(n-25) -3936032*a(n-26) -698645*a(n-27) +372159*a(n-28) -544552*a(n-29) +204304*a(n-30) +1076771*a(n-31) -228318*a(n-32) -350889*a(n-33) -45213*a(n-34) -145081*a(n-35) -12869*a(n-36) +57855*a(n-37) +11469*a(n-38) +6979*a(n-39) +1464*a(n-40) -851*a(n-41) -67*a(n-42) -54*a(n-43) -14*a(n-44) +2*a(n-45) -a(n-46)
%e Some solutions for n=4
%e ..1..1..1..1..0..0....0..1..1..1..1..1....1..1..0..0..1..1....1..1..0..1..1..0
%e ..1..1..1..0..0..0....0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..1..1..0
%e ..1..1..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..1..1..1..0
%e ..1..1..0..0..1..1....0..0..0..1..1..0....0..0..0..0..0..0....1..1..0..0..1..1
%e ..1..1..1..0..1..1....1..1..0..1..1..0....0..1..1..0..1..1....1..1..0..0..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2014