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A231839 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

%I A231839 #6 Jul 23 2025 06:43:22
%S A231839 4,4,16,16,50,64,50,188,422,256,144,760,4508,3823,1024,422,3309,52411,
%T A231839 111621,34350,4096,1268,14666,678660,3477361,2836554,308419,16384,
%U A231839 3823,64607,8887871,124132900,241961326,71178861,2771101,65536,11472,283479
%N A231839 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
%C A231839 Table starts
%C A231839 .......4..........4.............16.................50....................144
%C A231839 ......16.........50............188................760...................3309
%C A231839 ......64........422...........4508..............52411.................678660
%C A231839 .....256.......3823.........111621............3477361..............124132900
%C A231839 ....1024......34350........2836554..........241961326............24188209253
%C A231839 ....4096.....308419.......71178861........16599585680..........4666623161419
%C A231839 ...16384....2771101.....1792092360......1140658285204........899426070636904
%C A231839 ...65536...24892609....45099279326.....78428361897720.....173546274977761257
%C A231839 ..262144..223618304..1134900171250...5390322528656652...33474310504831841795
%C A231839 .1048576.2008825312.28560684486812.370517687958114665.6456965889651937136227
%H A231839 R. H. Hardin, <a href="/A231839/b231839.txt">Table of n, a(n) for n = 1..178</a>
%F A231839 Empirical for column k:
%F A231839 k=1: a(n) = 4*a(n-1)
%F A231839 k=2: a(n) = 4*a(n-1) +34*a(n-2) +86*a(n-3) +91*a(n-4) +46*a(n-5) +11*a(n-6) +a(n-7)
%F A231839 k=3: [order 10] for n>11
%F A231839 k=4: [order 29] for n>30
%F A231839 k=5: [order 82] for n>83
%F A231839 Empirical for row n:
%F A231839 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 A231839 n=2: [order 31] for n>32
%e A231839 Some solutions for n=3 k=4
%e A231839 ..3..2..2..2....2..2..3..2....2..2..0..0....3..3..1..0....0..0..0..3
%e A231839 ..0..0..3..0....2..3..2..2....3..0..0..1....2..1..0..0....0..0..1..1
%e A231839 ..0..0..0..1....2..2..2..3....1..2..2..2....1..1..1..2....2..2..2..2
%Y A231839 Column 1 is A000302
%Y A231839 Row 1 is A203094 for n>1
%K A231839 nonn,tabl
%O A231839 1,1
%A A231839 _R. H. Hardin_, Nov 14 2013