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A239405 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

%I A239405 #6 Jun 02 2025 09:27:48
%S A239405 2,4,5,8,23,12,16,105,129,28,32,478,1337,698,66,64,2165,13977,16449,
%T A239405 3805,156,128,9811,144762,394509,205969,20818,368,256,44399,1504399,
%U A239405 9340070,11334364,2590704,113774,868,512,201006,15591122,222457036,614216271
%N A239405 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.
%C A239405 Table starts
%C A239405 ....2.......4..........8............16................32...................64
%C A239405 ....5......23........105...........478..............2165.................9811
%C A239405 ...12.....129.......1337.........13977............144762..............1504399
%C A239405 ...28.....698......16449........394509...........9340070............222457036
%C A239405 ...66....3805.....205969......11334364.........614216271..........33522573911
%C A239405 ..156...20818....2590704.....326882784.......40566958960........5072216819342
%C A239405 ..368..113774...32507376....9402398952.....2671846338458......765206237815409
%C A239405 ..868..621754..408000104..270516990628...176044655676921...115478426410506313
%C A239405 .2048.3399032.5124790809.7789048968124.11610439554314901.17442858177037612521
%H A239405 R. H. Hardin, <a href="/A239405/b239405.txt">Table of n, a(n) for n = 1..180</a>
%F A239405 Empirical for column k:
%F A239405 k=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A239405 k=2: [order 16]
%F A239405 k=3: [order 64]
%F A239405 Empirical for row n:
%F A239405 n=1: a(n) = 2*a(n-1)
%F A239405 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 A239405 n=3: [order 25]
%F A239405 n=4: [order 91]
%e A239405 Some solutions for n=3 k=4
%e A239405 ..0..0..3..3....3..1..0..0....0..3..3..1....0..0..3..3....3..3..1..3
%e A239405 ..0..0..0..2....0..0..3..3....3..3..0..2....3..3..0..2....0..3..2..0
%e A239405 ..0..0..0..2....3..1..3..2....2..2..3..2....0..0..3..1....0..2..2..3
%Y A239405 Column 1 is A239333
%Y A239405 Row 1 is A000079
%K A239405 nonn,tabl
%O A239405 1,1
%A A239405 _R. H. Hardin_, Mar 17 2014