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A240327 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240327 #6 Jun 02 2025 09:49:21
%S A240327 2,2,2,4,5,4,6,17,17,6,8,37,116,37,8,14,80,455,455,80,14,20,213,1677,
%T A240327 3374,1677,213,20,30,443,8091,21455,21455,8091,443,30,48,1028,28448,
%U A240327 189549,247187,189549,28448,1028,48,70,2511,117304,1190246,3898804
%N A240327 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240327 Table starts
%C A240327 ..2....2.......4.........6............8............14............20
%C A240327 ..2....5......17........37...........80...........213...........443
%C A240327 ..4...17.....116.......455.........1677..........8091.........28448
%C A240327 ..6...37.....455......3374........21455........189549.......1190246
%C A240327 ..8...80....1677.....21455.......247187.......3898804......43979526
%C A240327 .14..213....8091....189549......3898804.....113751796....2343565571
%C A240327 .20..443...28448...1190246.....43979526....2343565571...88562956949
%C A240327 .30.1028..117304...8903613....602874070...58754628922.4085612680937
%C A240327 .48.2511..513841..70945972...8649395684.1550370290554
%C A240327 .70.5370.1871262.460466581.101952716878
%H A240327 R. H. Hardin, <a href="/A240327/b240327.txt">Table of n, a(n) for n = 1..111</a>
%F A240327 Empirical for column k:
%F A240327 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240327 k=2: [order 13] for n>14
%e A240327 Some solutions for n=4 k=4
%e A240327 ..3..2..3..2....3..2..3..3....2..3..3..2....3..2..2..2....3..2..3..2
%e A240327 ..2..1..2..3....2..1..2..2....3..0..1..3....2..1..1..1....2..3..2..1
%e A240327 ..3..1..3..2....3..2..2..0....3..1..1..2....3..0..2..2....3..0..0..2
%e A240327 ..2..3..2..2....3..2..2..2....2..3..3..2....3..2..2..2....3..2..0..0
%Y A240327 Column 1 is A239851
%K A240327 nonn,tabl
%O A240327 1,1
%A A240327 _R. H. Hardin_, Apr 03 2014