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A221663 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nX2 array.

%I A221663 #7 Jul 23 2025 02:06:08
%S A221663 2,12,48,256,856,4096,15872,65344,259584,1048576,4177632,16777216,
%T A221663 67051520,268430336,1073479680,4294967296,17178580480,68719476736,
%U A221663 274872664064,1099511513088,4398023442432,17592186044416,70368641459200
%N A221663 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nX2 array.
%C A221663 Column 2 of A221666
%H A221663 R. H. Hardin, <a href="/A221663/b221663.txt">Table of n, a(n) for n = 1..210</a>
%F A221663 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 A221663 Some solutions for n=3
%e A221663 ..0..0....0..0....1..0....0..0....0..1....0..0....0..0....1..1....1..0....1..1
%e A221663 ..1..1....0..1....1..1....0..1....1..0....1..1....1..0....1..0....0..0....0..0
%e A221663 ..1..0....0..1....0..0....0..0....0..0....0..1....1..1....1..1....0..1....1..1
%K A221663 nonn
%O A221663 1,1
%A A221663 _R. H. Hardin_ Jan 21 2013