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A231940 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

%I A231940 #6 Jul 23 2025 06:44:23
%S A231940 4,4,16,16,84,64,50,668,318,256,144,5070,8426,1328,1024,422,42104,
%T A231940 206808,152180,6064,4096,1268,326010,4736026,11159202,2462572,26918,
%U A231940 16384,3823,2511252,94464137,691418144,518972238,36885538,116909,65536,11472
%N A231940 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.
%C A231940 Table starts
%C A231940 .......4.......4............16...............50................144
%C A231940 ......16......84...........668.............5070..............42104
%C A231940 ......64.....318..........8426...........206808............4736026
%C A231940 .....256....1328........152180.........11159202..........691418144
%C A231940 ....1024....6064.......2462572........518972238........86074040354
%C A231940 ....4096...26918......36885538......23280281589.....10417626293694
%C A231940 ...16384..116909.....586971925....1098832065447...1320620287047433
%C A231940 ...65536..511264....9394148948...52087504055935.167980047970274816
%C A231940 ..262144.2248196..147360195020.2432351670277323
%C A231940 .1048576.9868600.2323912599668
%H A231940 R. H. Hardin, <a href="/A231940/b231940.txt">Table of n, a(n) for n = 1..84</a>
%F A231940 Empirical for column k:
%F A231940 k=1: a(n) = 4*a(n-1)
%F A231940 k=2: [order 19] for n>20
%F A231940 k=3: [order 65] for n>66
%F A231940 Empirical for row n:
%F A231940 n=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8
%F A231940 n=2: [order 15]
%e A231940 Some solutions for n=3 k=4
%e A231940 ..0..0..0..1....0..0..0..3....2..0..0..2....0..2..2..1....0..0..1..0
%e A231940 ..2..0..2..2....3..0..0..3....3..3..0..0....3..0..0..2....2..0..0..3
%e A231940 ..2..3..0..0....1..2..3..0....1..0..0..2....2..0..0..0....0..2..3..2
%Y A231940 Column 1 is A000302
%Y A231940 Column 2 is A231741
%Y A231940 Row 1 is A203094 for n>1
%K A231940 nonn,tabl
%O A231940 1,1
%A A231940 _R. H. Hardin_, Nov 15 2013