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A183374 T(n,k)=Number of nXk binary arrays with no element equal to the mod 3 sum of its diagonal and antidiagonal neighbors.

%I A183374 #7 Jul 22 2025 08:53:08
%S A183374 1,1,1,1,4,1,1,4,4,1,1,9,6,9,1,1,16,16,16,16,1,1,25,30,49,30,25,1,1,
%T A183374 49,64,64,64,64,49,1,1,81,165,144,195,144,165,81,1,1,144,361,729,625,
%U A183374 625,729,361,144,1,1,256,875,2304,2580,3969,2580,2304,875,256,1,1,441,2116
%N A183374 T(n,k)=Number of nXk binary arrays with no element equal to the mod 3 sum of its diagonal and antidiagonal neighbors.
%C A183374 Table starts
%C A183374 .1...1....1.....1......1.......1.........1..........1...........1.............1
%C A183374 .1...4....4.....9.....16......25........49.........81.........144...........256
%C A183374 .1...4....6....16.....30......64.......165........361.........875..........2116
%C A183374 .1...9...16....49.....64.....144.......729.......2304........6724.........22500
%C A183374 .1..16...30....64....195.....625......2580.......8836.......34903........148996
%C A183374 .1..25...64...144....625....3969.....22801.....104329......580644.......3763600
%C A183374 .1..49..165...729...2580...22801....285516....1999396....15732530.....141039376
%C A183374 .1..81..361..2304...8836..104329...1999396...22743361...233203441....2719518201
%C A183374 .1.144..875..6724..34903..580644..15732530..233203441..3414837564...58892126329
%C A183374 .1.256.2116.22500.148996.3763600.141039376.2719518201.58892126329.1467194393284
%H A183374 R. H. Hardin, <a href="/A183374/b183374.txt">Table of n, a(n) for n = 1..337</a>
%e A183374 Some solutions for 6X5
%e A183374 ..0..1..0..0..1....1..1..0..1..0....0..0..1..1..0....0..0..1..1..0
%e A183374 ..0..1..0..0..1....0..0..0..1..0....1..1..0..1..0....1..1..0..1..0
%e A183374 ..0..0..0..0..1....0..0..1..0..1....0..0..1..0..0....0..0..1..1..0
%e A183374 ..1..0..0..0..0....0..1..1..1..0....0..0..1..0..0....0..0..0..0..0
%e A183374 ..1..0..0..1..0....0..1..1..1..0....1..1..0..1..0....0..1..0..0..0
%e A183374 ..1..0..0..1..0....0..0..1..0..0....0..0..1..1..0....0..1..0..1..1
%Y A183374 Column 2 is A133037(n+6)
%K A183374 nonn,tabl
%O A183374 1,5
%A A183374 _R. H. Hardin_ Jan 04 2011