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A240284 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240284 #6 Jun 02 2025 09:46:41
%S A240284 1,2,2,2,8,3,4,19,19,4,4,76,80,38,7,8,181,570,262,114,10,8,741,2574,
%T A240284 3457,1461,251,15,16,1779,20764,28654,33183,5443,612,24,16,7308,97348,
%U A240284 443168,484146,218658,24490,1656,35,32,17561,802835,3980245,13490093,5646644
%N A240284 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240284 Table starts
%C A240284 ..1....2.......2.........4............4.............8..............8
%C A240284 ..2....8......19........76..........181...........741...........1779
%C A240284 ..3...19......80.......570.........2574.........20764..........97348
%C A240284 ..4...38.....262......3457........28654........443168........3980245
%C A240284 ..7..114....1461.....33183.......484146......13490093......224906182
%C A240284 .10..251....5443....218658......5646644.....281488213.....8597299482
%C A240284 .15..612...24490...1851080.....88953626....8199368365...463717321235
%C A240284 .24.1656..117962..15760838...1357879302..225885684501.23104690637116
%C A240284 .35.3758..459193.110599613..17350066110.5291794810655
%C A240284 .54.9630.2147788.945852472.272318368893
%H A240284 R. H. Hardin, <a href="/A240284/b240284.txt">Table of n, a(n) for n = 1..111</a>
%F A240284 Empirical for column k:
%F A240284 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240284 k=2: [order 15]
%F A240284 Empirical for row n:
%F A240284 n=1: a(n) = 2*a(n-2)
%F A240284 n=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
%F A240284 n=3: [order 48] for n>51
%e A240284 Some solutions for n=4 k=4
%e A240284 ..3..1..3..3....3..3..1..1....3..1..3..3....3..1..3..1....3..1..3..1
%e A240284 ..3..1..3..2....3..2..1..2....3..1..0..0....3..2..0..1....2..2..2..0
%e A240284 ..3..1..3..2....2..0..2..2....2..2..2..0....3..2..3..2....2..0..0..1
%e A240284 ..2..2..2..0....3..1..0..0....3..1..0..0....2..2..3..3....3..3..0..2
%Y A240284 Column 1 is A159288
%Y A240284 Row 1 is A016116
%K A240284 nonn,tabl
%O A240284 1,2
%A A240284 _R. H. Hardin_, Apr 03 2014