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A239649 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

%I A239649 #6 Jun 02 2025 09:30:54
%S A239649 2,4,4,8,20,10,16,92,112,22,32,418,1182,560,50,64,1898,12246,13476,
%T A239649 2874,114,128,8588,127454,320314,158728,14788,258,256,38888,1320102,
%U A239649 7629186,8634040,1864886,75540,586,512,175974,13703468,181039448,471203608
%N A239649 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.
%C A239649 Table starts
%C A239649 ....2.......4..........8............16...............32...................64
%C A239649 ....4......20.........92...........418.............1898.................8588
%C A239649 ...10.....112.......1182.........12246...........127454..............1320102
%C A239649 ...22.....560......13476........320314..........7629186............181039448
%C A239649 ...50....2874.....158728.......8634040........471203608..........25594620082
%C A239649 ..114...14788....1864886.....232304146......29007348454........3608789598890
%C A239649 ..258...75540...21813374....6219477628....1778793691226......506611939408296
%C A239649 ..586..387306..255830770..167002115382..109328664988704....71303275040032094
%C A239649 .1330.1983686.2997975560.4480024646968.6715782662219974.10028169382114414238
%H A239649 R. H. Hardin, <a href="/A239649/b239649.txt">Table of n, a(n) for n = 1..180</a>
%F A239649 Empirical for column k:
%F A239649 k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
%F A239649 k=2: [order 10]
%F A239649 k=3: [order 35]
%F A239649 Empirical for row n:
%F A239649 n=1: a(n) = 2*a(n-1)
%F A239649 n=2: a(n) = 3*a(n-1) +12*a(n-2) -18*a(n-3) -29*a(n-4) +19*a(n-5) +38*a(n-6) +8*a(n-7)
%F A239649 n=3: [order 25]
%F A239649 n=4: [order 91]
%e A239649 Some solutions for n=3 k=4
%e A239649 ..3..1..3..1....3..0..1..3....1..0..3..3....3..0..0..0....1..0..3..3
%e A239649 ..2..1..2..0....2..1..1..2....1..0..3..3....2..0..3..0....1..3..2..0
%e A239649 ..1..3..1..0....2..1..1..1....1..0..3..3....2..1..2..3....1..0..0..0
%Y A239649 Column 1 is A078040
%Y A239649 Row 1 is A000079
%K A239649 nonn,tabl
%O A239649 1,1
%A A239649 _R. H. Hardin_, Mar 23 2014