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T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors
5

%I #5 Mar 31 2012 12:35:51

%S 1,1,1,1,1,1,2,1,1,2,3,2,1,2,3,5,3,2,2,3,5,8,5,3,4,3,5,8,13,8,5,8,8,5,

%T 8,13,21,13,8,16,21,16,8,13,21,34,21,13,36,49,49,36,13,21,34,55,34,21,

%U 74,136,148,136,74,21,34,55,89,55,34,156,355,526,526,355,156,34,55,89,144

%N T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors

%C Table starts

%C ..1..1..1...2....3.....5......8......13.......21........34........55.........89

%C ..1..1..1...2....3.....5......8......13.......21........34........55.........89

%C ..1..1..1...2....3.....5......8......13.......21........34........55.........89

%C ..2..2..2...4....8....16.....36......74......156.......334.......706.......1504

%C ..3..3..3...8...21....49....136.....355......933......2502......6653......17823

%C ..5..5..5..16...49...148....526....1683.....5607.....18936.....63278.....214169

%C ..8..8..8..36..136...526...2376....9630....40630....173846....732918....3140616

%C .13.13.13..74..355..1683...9630...48868...259143...1401296...7444267...40309363

%C .21.21.21.156..933..5607..40630..259143..1730057..11807846..78983225..539945053

%C .34.34.34.334.2502.18936.173846.1401296.11807846.102043638.861956606.7453821796

%H R. H. Hardin, <a href="/A183391/b183391.txt">Table of n, a(n) for n = 1..312</a>

%e Some solutions with a(1,1)=0 for 6X5

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

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

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

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

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

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

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Jan 04 2011