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 A203272 Number of nX3 0..5 arrays with every nonzero element less than or equal to some NW, E or S neighbor 1

%I #5 Mar 31 2012 12:36:56

%S 1,861,107968,7849844,525063657,38204132307,2854004857534,

%T 209528571255971,15268341534543913,1116005261918179242,

%U 81729420101718397601,5982387762928460622575,437688956165613139223655

%N Number of nX3 0..5 arrays with every nonzero element less than or equal to some NW, E or S neighbor

%C Column 3 of A203277

%H R. H. Hardin, <a href="/A203272/b203272.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 216*a(n-1) -21155*a(n-2) +1341860*a(n-3) -62837724*a(n-4) +2275016080*a(n-5) -64927321638*a(n-6) +1485554695463*a(n-7) -27773283232101*a(n-8) +432693095852266*a(n-9) -5723034591098916*a(n-10) +65346955996986838*a(n-11) -653496810906847470*a(n-12) +5791211105249921520*a(n-13) -45866353775989123889*a(n-14) +326293737844255332644*a(n-15) -2089144918621577469816*a(n-16) +12036772890599751621413*a(n-17) -62336594746251148761698*a(n-18) +289827254704694951871676*a(n-19) -1208764311836075167020757*a(n-20) +4520906832197187066336036*a(n-21) -15166321689080888357946560*a(n-22) +45663695605667094369585207*a(n-23) -123512286135059771326395903*a(n-24) +300494700654034270815805553*a(n-25) -658550383792649822709808416*a(n-26) +1302094470253456820240369336*a(n-27) -2325937230872094919307628660*a(n-28) +3756768217858989360710603332*a(n-29) -5485450079928492933298248688*a(n-30) +7229282617191750675038321360*a(n-31) -8571195823801127561238894656*a(n-32) +9096886032877779398877798016*a(n-33) -8586694793904850994874099136*a(n-34) +7152471889144227041839003712*a(n-35) -5210877672869220856193481472*a(n-36) +3287222945668229226077351168*a(n-37) -1775222513503967422779784704*a(n-38) +809814164000539729056943104*a(n-39) -307025749536635431945943040*a(n-40) +94759218163927616947384320*a(n-41) -23151871326857825811456000*a(n-42) +4300773845864077107855360*a(n-43) -569858048873108063354880*a(n-44) +47912648791741267968000*a(n-45) -1918937765676987187200*a(n-46) for n>48

%e Some solutions for n=4

%e ..3..5..0....1..5..3....5..0..4....4..5..2....2..2..0....2..1..5....5..4..0

%e ..3..5..4....4..5..3....5..4..4....4..5..2....1..2..3....4..4..5....5..4..3

%e ..5..5..4....2..5..1....5..0..4....5..5..2....5..4..3....5..5..5....5..3..2

%e ..5..5..3....5..5..5....5..5..0....3..5..5....5..5..3....1..2..5....5..5..0

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 31 2011

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