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%I #4 Dec 06 2012 16:23:34
%S 2,16,48,256,856,4096,15872,65536,259584,1048576,4177632,16777216,
%T 67051520,268435456,1073479680,4294967296,17178580480,68719476736,
%U 274872664064,1099511627776,4398023442432,17592186044416,70368641459200
%N Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX2 array
%C Column 2 of A220177
%H R. H. Hardin, <a href="/A220173/b220173.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +8*a(n-2) -32*a(n-3) -16*a(n-4) +64*a(n-5) +52*a(n-6) -208*a(n-7) -416*a(n-8) +1664*a(n-9) +832*a(n-10) -3328*a(n-11) -1056*a(n-12) +4224*a(n-13) +8448*a(n-14) -33792*a(n-15) -16896*a(n-16) +67584*a(n-17) +10880*a(n-18) -43520*a(n-19) -87040*a(n-20) +348160*a(n-21) +174080*a(n-22) -696320*a(n-23) -62720*a(n-24) +250880*a(n-25) +501760*a(n-26) -2007040*a(n-27) -1003520*a(n-28) +4014080*a(n-29) +205824*a(n-30) -823296*a(n-31) -1646592*a(n-32) +6586368*a(n-33) +3293184*a(n-34) -13172736*a(n-35) -360448*a(n-36) +1441792*a(n-37) +2883584*a(n-38) -11534336*a(n-39) -5767168*a(n-40) +23068672*a(n-41) +262144*a(n-42) -1048576*a(n-43) -2097152*a(n-44) +8388608*a(n-45) +4194304*a(n-46) -16777216*a(n-47)
%e Some solutions for n=3
%e ..0..1....1..1....0..0....0..0....1..0....0..1....1..0....1..0....0..1....0..0
%e ..1..0....0..0....1..1....0..0....1..1....1..0....0..1....1..1....1..1....1..1
%e ..1..0....0..0....1..1....1..0....0..1....0..1....0..0....1..0....1..0....0..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 06 2012