A251219 - OEIS

%I #4 Nov 30 2014 20:22:06

%S 9,21,21,49,63,49,115,191,191,115,269,589,758,589,269,631,1807,3089,

%T 3089,1807,631,1477,5569,12503,16911,12503,5569,1477,3463,17119,50912,

%U 91777,91777,50912,17119,3463,8109,52713,206715,502971,666522,502971,206715

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having zero or two 1s

%C Table starts

%C .....9.....21.......49.......115.........269..........631...........1477

%C ....21.....63......191.......589........1807.........5569..........17119

%C ....49....191......758......3089.......12503........50912.........206715

%C ...115....589.....3089.....16911.......91777.......502971........2746607

%C ...269...1807....12503.....91777......666522......4907873.......35978029

%C ...631...5569....50912....502971.....4907873.....48781920......482274751

%C ..1477..17119...206715...2746607....35978029....482274751.....6424279907

%C ..3463..52713...840931..15040763...264753513...4791965557....86110233175

%C ..8109.162143..3417338..82261821..1945208633..47523048960..1151625700234

%C .19007.499081.13896689.450304289.14308155872.471984045011.15428988432635

%H R. H. Hardin, <a href="/A251219/b251219.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +4*a(n-2) -2*a(n-3)

%F k=2: a(n) = 3*a(n-1) +4*a(n-2) -12*a(n-3) +4*a(n-5)

%F k=3: [order 9]

%F k=4: [order 16]

%F k=5: [order 32]

%F k=6: [order 62]

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 30 2014