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A220177 T(n,k)=Sum of neighbor maps: number of nXk 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 nXk array.

%I A220177 #7 Jul 23 2025 00:55:03
%S A220177 2,2,2,8,16,8,16,48,48,16,24,256,404,256,24,64,856,4096,4096,856,64,
%T A220177 128,4096,31744,65536,31744,4096,128,232,15872,262144,1048576,1048576,
%U A220177 262144,15872,232,512,65536,2083808,16777216,32395806,16777216,2083808,65536
%N A220177 T(n,k)=Sum of neighbor maps: number of nXk 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 nXk array.
%C A220177 Table starts
%C A220177 ....2......2........8........16.........24.........64.........128........232
%C A220177 ....2.....16.......48.......256........856.......4096.......15872......65536
%C A220177 ....8.....48......404......4096......31744.....262144.....2083808...16728064
%C A220177 ...16....256.....4096.....65536....1048576...16777216...268435456.4294967296
%C A220177 ...24....856....31744...1048576...32395806.1073741824.34351349760
%C A220177 ...64...4096...262144..16777216.1073741824
%C A220177 ..128..15872..2083808.268435456
%C A220177 ..232..65536.16728064
%C A220177 ..512.259584
%C A220177 .1024
%C A220177 T(n,4)=16^n for n<=8 but not for n=9, so T(n,6) is unlikely to be 64^n for long
%H A220177 R. H. Hardin, <a href="/A220177/b220177.txt">Table of n, a(n) for n = 1..60</a>
%e A220177 Some solutions for n=3 k=4
%e A220177 ..0..1..1..0....1..0..0..1....0..0..1..1....0..1..0..0....0..1..1..1
%e A220177 ..0..1..1..1....1..0..1..1....1..0..1..0....0..0..1..1....1..1..1..1
%e A220177 ..0..1..1..0....1..0..1..0....1..1..0..1....1..1..0..1....0..0..0..0
%K A220177 nonn,tabl
%O A220177 1,1
%A A220177 _R. H. Hardin_ Dec 06 2012