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A206692 T(n,k)=Number of nXk 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.

%I A206692 #7 Jul 22 2025 19:36:56
%S A206692 1,1,1,1,4,1,2,11,11,2,4,36,44,36,4,8,116,176,176,116,8,16,376,704,
%T A206692 916,704,376,16,32,1216,2816,4704,4704,2816,1216,32,64,3936,11264,
%U A206692 24492,31504,24492,11264,3936,64,128,12736,45056,127008,213788,213788,127008
%N A206692 T(n,k)=Number of nXk 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
%C A206692 Table starts
%C A206692 ..1....1.....1......2.......4.........8.........16..........32...........64
%C A206692 ..1....4....11.....36.....116.......376.......1216........3936........12736
%C A206692 ..1...11....44....176.....704......2816......11264.......45056.......180224
%C A206692 ..2...36...176....916....4704.....24492.....127008......660888......3436488
%C A206692 ..4..116...704...4704...31504....213788....1454810.....9933294.....67923354
%C A206692 ..8..376..2816..24492..213788...1915580...17277556...156946368...1429962032
%C A206692 .16.1216.11264.127008.1454810..17277556..208563912..2543024548..31198656992
%C A206692 .32.3936.45056.660888.9933294.156946368.2543024548.41832855136.694325337444
%H A206692 R. H. Hardin, <a href="/A206692/b206692.txt">Table of n, a(n) for n = 1..199</a>
%e A206692 Some solutions for n=4 k=3
%e A206692 ..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
%e A206692 ..2..3..0....3..0..1....1..2..3....1..2..3....3..2..1....1..2..3....1..3..0
%e A206692 ..1..2..3....1..2..3....2..0..1....2..3..1....2..0..3....2..3..0....2..0..1
%e A206692 ..3..0..1....0..3..2....3..1..2....0..1..2....0..1..2....0..1..2....3..1..2
%Y A206692 Column 3 is A002089(n-2)
%K A206692 nonn,tabl
%O A206692 1,5
%A A206692 _R. H. Hardin_ Feb 11 2012