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%I #4 Jan 15 2014 09:22:18
%S 141,977,6882,41446,242684,1310058,6840001,34087789,165068548,
%T 775598494,3562426975,16017777604,70763909432,307697458346,
%U 1319740103323,5591683329070,23438083323919,97303006036084,400509298117315
%N Number of (n+1)X(3+1) 0..1 arrays with the sum of each 2X2 subblock two median terms lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Column 3 of A235765
%H R. H. Hardin, <a href="/A235760/b235760.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 21*a(n-1) -154*a(n-2) +216*a(n-3) +3102*a(n-4) -15362*a(n-5) -8010*a(n-6) +227638*a(n-7) -346453*a(n-8) -1667959*a(n-9) +5293502*a(n-10) +5913596*a(n-11) -40977903*a(n-12) +4490375*a(n-13) +207977376*a(n-14) -176830602*a(n-15) -745036126*a(n-16) +1113969734*a(n-17) +1909476924*a(n-18) -4364931308*a(n-19) -3327846891*a(n-20) +12414234111*a(n-21) +2926950230*a(n-22) -27049487256*a(n-23) +3161362257*a(n-24) +46248491955*a(n-25) -17923984610*a(n-26) -62647257108*a(n-27) +39042123170*a(n-28) +67187956474*a(n-29) -57699545498*a(n-30) -56372293146*a(n-31) +64098745925*a(n-32) +35855979111*a(n-33) -55387030614*a(n-34) -15906775348*a(n-35) +37647675071*a(n-36) +3461774001*a(n-37) -20115999844*a(n-38) +1185897478*a(n-39) +8365429502*a(n-40) -1543037022*a(n-41) -2652640376*a(n-42) +792816240*a(n-43) +618128251*a(n-44) -258968623*a(n-45) -98545950*a(n-46) +57118960*a(n-47) +8963328*a(n-48) -8298400*a(n-49) -107584*a(n-50) +720640*a(n-51) -63232*a(n-52) -28416*a(n-53) +4608*a(n-54)
%e Some solutions for n=4
%e ..0..1..1..1....0..1..1..1....1..1..1..1....0..1..1..1....1..0..1..1
%e ..0..1..1..1....0..1..1..1....0..1..0..1....1..1..1..1....1..1..1..1
%e ..0..0..0..1....0..0..1..1....1..0..1..0....1..0..1..0....0..1..1..0
%e ..0..0..0..0....1..0..0..1....1..0..1..0....0..0..1..0....0..0..0..1
%e ..1..0..0..0....0..0..0..0....0..0..0..1....0..0..1..0....0..0..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 15 2014
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