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%I #13 Jun 13 2020 01:50:04
%S 1,1,1,2,1,2,2,2,2,2,3,4,7,4,3,4,6,17,17,6,4,5,10,41,59,41,10,5,7,18,
%T 97,205,205,97,18,7,9,30,235,724,952,724,235,30,9,12,50,607,2466,4654,
%U 4654,2466,607,50,12,16,86,1415,8948,23083,32411,23083,8948,1415,86,16,21,146
%N T(n,k) is the number of n X k 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.
%C Table starts
%C .1..1...2....2......3.......4........5.........7..........9..........12
%C .1..1...2....4......6......10.......18........30.........50..........86
%C .2..2...7...17.....41......97......235.......607.......1415........3486
%C .2..4..17...59....205.....724.....2466......8948......30945......108083
%C .3..6..41..205....952....4654....23083....115377.....551208.....2757161
%C .4.10..97..724...4654...32411...223567...1625772...10889470....76035931
%C .5.18.235.2466..23083..223567..2208945..22411843..216858412..2141041521
%C .7.30.607.8948.115377.1625772.22411843.323885934.4389100997.61921804090
%H R. H. Hardin, <a href="/A203181/b203181.txt">Table of n, a(n) for n = 1..364</a>
%e Some solutions for n=5 k=3
%e ..0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2
%e ..1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
%e ..2..1..2....2..1..0....2..1..2....0..1..0....0..1..2....0..1..2....0..1..0
%e ..0..1..2....0..1..2....0..1..0....1..2..1....1..2..0....1..2..0....1..2..1
%e ..1..0..1....1..0..1....1..0..1....2..0..1....0..1..1....0..1..1....2..0..1
%Y Column 1 is A000931(n+5). Column 2 is A203175.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 30 2011