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T(n,k)=Number of city-block distance 1, pressure limit 2 movements in an nXk array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops
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%I #4 Sep 21 2012 17:04:31

%S 0,0,0,0,2,0,0,14,14,0,0,80,264,80,0,0,436,4794,4794,436,0,0,2346,

%T 83304,280900,83304,2346,0,0,12578,1435808,15836932,15836932,1435808,

%U 12578,0,0,67368,24673352,886416182,2891592224,886416182,24673352,67368,0,0,360720

%N T(n,k)=Number of city-block distance 1, pressure limit 2 movements in an nXk array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops

%C Table starts

%C .0........0..............0....................0..........................0

%C .0........2.............14...................80........................436

%C .0.......14............264.................4794......................83304

%C .0.......80...........4794...............280900...................15836932

%C .0......436..........83304.............15836932.................2891592224

%C .0.....2346........1435808............886416182...............524266454832

%C .0....12578.......24673352..........49491906456.............94821314531592

%C .0....67368......423651134........2761454361344..........17138656649477498

%C .0...360720.....7272419728......154047246448662........3097157052139827164

%C .0..1931306...124829530972.....8592994055896310......559661504116914345352

%C .0.10340030..2142624332680...479322218408145970...101130124206092104688984

%C .0.55359176.36776621687102.26736736612809407136.18273998071786696959934276

%H R. H. Hardin, <a href="/A216991/b216991.txt">Table of n, a(n) for n = 1..241</a>

%e Some solutions for n=3 k=4 (movement: 0=n 1=e 2=s 3=w)

%e ..1..1..2..3....1..1..1..2....2..3..3..3....2..2..2..2....1..2..1..2

%e ..0..0..1..0....0..1..2..2....2..0..1..0....1..2..2..3....2..3..0..3

%e ..1..1..1..0....0..3..3..3....1..1..1..0....0..3..3..3....1..0..3..0

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Sep 21 2012