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%I #4 Dec 30 2014 19:56:08
%S 2500,22877,219438,1027387,5829147,21245477,92753092,299160892,
%T 1126530715,3407488838,11740231069,34352248435,112041051335,
%U 322932426766,1018089749261,2922063885711,9022892348437,25949732507316,79139400390836
%N Number of (n+1)X(3+1) 0..2 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw
%C Column 3 of A253375
%H R. H. Hardin, <a href="/A253370/b253370.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) +18*a(n-2) -390*a(n-3) +363*a(n-4) +7557*a(n-5) -16924*a(n-6) -85080*a(n-7) +289038*a(n-8) +592626*a(n-9) -3022596*a(n-10) -2302692*a(n-11) +22010974*a(n-12) +263586*a(n-13) -118108608*a(n-14) +60625464*a(n-15) +480363315*a(n-16) -453795339*a(n-17) -1497838078*a(n-18) +2041953882*a(n-19) +3566209239*a(n-20) -6619257735*a(n-21) -6304597140*a(n-22) +16357594512*a(n-23) +7550240128*a(n-24) -31527338352*a(n-25) -3791317152*a(n-26) +47758481952*a(n-27) -6659648352*a(n-28) -56728278048*a(n-29) +20129722880*a(n-30) +52207707264*a(n-31) -28856183808*a(n-32) -36302235648*a(n-33) +27669476352*a(n-34) +18144427008*a(n-35) -18828638464*a(n-36) -5799153408*a(n-37) +9055982592*a(n-38) +719677440*a(n-39) -2944438272*a(n-40) +244629504*a(n-41) +582598656*a(n-42) -119439360*a(n-43) -53084160*a(n-44) +15925248*a(n-45) for n>48
%e Some solutions for n=2
%e ..0..1..2..1....1..1..1..2....0..2..0..2....0..0..0..1....1..0..1..0
%e ..2..1..2..1....1..1..1..0....0..0..1..0....1..0..2..0....1..1..1..2
%e ..2..2..2..2....2..0..2..2....2..1..1..1....1..2..2..2....1..0..2..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2014
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