%I #7 Oct 06 2015 22:00:39
%S 2,5,5,12,17,12,29,54,54,29,70,174,224,174,70,169,559,950,950,559,169,
%T 408,1797,4012,5362,4012,1797,408,985,5776,16964,30113,30113,16964,
%U 5776,985,2378,18566,71712,169560,224640,169560,71712,18566,2378,5741,59677
%N T(n,k) = 1/20 of the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease.
%C Table starts
%C ....2......5......12........29.........70..........169...........408
%C ....5.....17......54.......174........559.........1797..........5776
%C ...12.....54.....224.......950.......4012........16964.........71712
%C ...29....174.....950......5362......30113.......169560........954496
%C ...70....559....4012.....30113.....224640......1683197......12606120
%C ..169...1797...16964....169560....1683197.....16823812.....168070828
%C ..408...5776...71712....954496...12606120....168070828....2239265280
%C ..985..18566..303170...5374440...94463507...1680902120...29887741084
%C .2378..59677.1281664..30261345..707826798..16810325640..398877017736
%C .5741.191821.5418314.170394226.5304230928.168150768145.5325395568832
%H R. H. Hardin, <a href="/A183719/b183719.txt">Table of n, a(n) for n = 1..363</a>
%e Some solutions for 4 X 3:
%e ..3..0..4....3..0..4....1..4..1....0..1..4....3..4..3....1..2..1....2..1..2
%e ..2..1..2....2..1..2....2..3..2....4..2..3....2..0..1....4..3..0....3..0..4
%e ..3..0..4....3..4..3....0..4..0....0..1..0....3..4..3....1..2..1....2..1..2
%e ..2..1..3....2..1..2....2..3..1....3..2..3....2..1..2....0..3..4....3..0..3
%e ...
%e ...R..L.......R..L.......L..R.......R..L.......R..L.......R..L.......L..R...
%e ...L..R.......L..R.......R..L.......L..R.......L..R.......L..R.......R..L...
%e ...R..L.......R..L.......L..R.......R..L.......R..L.......R..L.......L..R...
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 06 2011