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T(n,k)=Number of nXk binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically
8

%I #5 Mar 31 2012 12:36:52

%S 1,2,2,4,12,4,7,50,50,7,12,188,398,188,12,21,724,3018,3018,724,21,37,

%T 2820,23436,45519,23436,2820,37,65,10960,182430,702846,702846,182430,

%U 10960,65,114,42544,1417772,10892633,21649928,10892633,1417772,42544,114

%N T(n,k)=Number of nXk binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically

%C Table starts

%C ...1......2.........4............7..............12.................21

%C ...2.....12........50..........188.............724...............2820

%C ...4.....50.......398.........3018...........23436.............182430

%C ...7....188......3018........45519..........702846...........10892633

%C ..12....724.....23436.......702846........21649928..........669872090

%C ..21...2820....182430.....10892633.......669872090........41382940317

%C ..37..10960...1417772....168585867.....20696263392......2552520578945

%C ..65..42544..11017196...2608652667....639259508770....157398925950921

%C .114.165176..85621362..40368680378..19746821708510...9706685199080140

%C .200.641376.665418194.624709738658.609991818060458.598614098605286252

%H R. H. Hardin, <a href="/A202795/b202795.txt">Table of n, a(n) for n = 1..480</a>

%e Some solutions for n=5 k=3

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

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

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

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

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

%Y Column 1 is A005251(n+2)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Dec 24 2011