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%I #6 Jan 20 2024 17:58:03
%S 2,3,3,6,5,6,11,15,15,11,22,33,90,33,22,43,99,351,351,99,43,86,261,
%T 2106,2399,2106,261,86,171,783,10935,26131,26131,10935,783,171,342,
%U 2241,65610,252097,570922,252097,65610,2241,342,683,6723,378351,2767631,10789339
%N T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.
%C Table starts
%C ...2.....3........6.........11............22...............43
%C ...3.....5.......15.........33............99..............261
%C ...6....15.......90........351..........2106............10935
%C ..11....33......351.......2399.........26131...........252097
%C ..22....99.....2106......26131........570922.........10789339
%C ..43...261....10935.....252097......10789339........394241389
%C ..86...783....65610....2767631.....237172426......16940254423
%C .171..2241...378351...29452071....5028462531.....699094613961
%C .342..6723..2270106..323841891..110616890922...30056993215803
%C .683.19845.13482855.3532758473.2411745951979.1279198648576981
%H R. H. Hardin, <a href="/A262332/b262332.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F k=2: a(n) = 3*a(n-1) +3*a(n-2) -9*a(n-3)
%F k=3: a(n) = 6*a(n-1) +9*a(n-2) -54*a(n-3)
%F k=4: [order 7]
%F k=5: [order 11]
%F k=6: [order 15]
%F k=7: [order 19]
%e Some solutions for n=4, k=4
%e ..0..0..0..0..0....0..1..1..1..1....1..1..0..1..1....0..0..0..1..1
%e ..1..1..1..1..0....1..1..0..0..0....1..0..1..0..1....1..1..0..1..1
%e ..1..1..1..1..0....1..1..1..1..0....1..0..0..1..0....1..0..0..1..0
%e ..1..1..0..0..0....0..1..0..0..1....1..1..0..0..0....0..0..0..1..1
%e ..1..1..0..0..0....0..0..1..1..0....0..0..1..1..0....0..1..0..0..1
%Y Column 1 is A005578(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Sep 18 2015