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A259250 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0111.

%I A259250 #6 Jun 02 2025 11:50:01
%S A259250 9,21,21,48,65,48,111,192,192,111,255,581,720,581,255,588,1733,2816,
%T A259250 2816,1733,588,1353,5216,10720,14425,10720,5216,1353,3117,15613,41552,
%U A259250 71313,71313,41552,15613,3117,7176,46897,159168,361728,451481,361728,159168
%N A259250 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0111.
%C A259250 Table starts
%C A259250 .....9.....21......48.......111........255..........588..........1353
%C A259250 ....21.....65.....192.......581.......1733.........5216.........15613
%C A259250 ....48....192.....720......2816......10720........41552........159168
%C A259250 ...111....581....2816.....14425......71313.......361728.......1803859
%C A259250 ...255...1733...10720.....71313.....451481......2964676......18970267
%C A259250 ...588...5216...41552....361728....2964676.....25462352.....211569948
%C A259250 ..1353..15613..159168...1803859...18970267....211569948....2259371001
%C A259250 ..3117..46897..614560...9106657..123694345...1802996568...24946035357
%C A259250 ..7176.140568.2360464..45601304..795726064..15090948960..268635598788
%C A259250 .16527.421901.9098240.229700941.5169185873.128059095616.2948447364239
%H A259250 R. H. Hardin, <a href="/A259250/b259250.txt">Table of n, a(n) for n = 1..449</a>
%F A259250 Empirical for column k:
%F A259250 k=1: a(n) = a(n-1) +3*a(n-2)
%F A259250 k=2: a(n) = 3*a(n-1) +4*a(n-2) -11*a(n-3) -3*a(n-4)
%F A259250 k=3: a(n) = 2*a(n-1) +12*a(n-2) -11*a(n-3) -30*a(n-4)
%F A259250 k=4: [order 11]
%F A259250 k=5: [order 17]
%F A259250 k=6: [order 31]
%F A259250 k=7: [order 54]
%e A259250 Some solutions for n=4 k=4
%e A259250 ..0..1..1..1..1....0..1..0..0..1....0..1..0..1..1....0..1..1..1..1
%e A259250 ..1..1..0..1..0....1..1..1..1..1....0..1..1..1..0....0..1..0..0..0
%e A259250 ..0..1..1..1..0....0..0..1..0..1....0..1..0..1..1....1..1..1..1..1
%e A259250 ..0..1..0..1..0....1..1..1..1..1....1..1..1..1..0....1..0..0..0..1
%e A259250 ..0..1..0..1..0....1..0..0..1..0....1..0..0..1..1....1..0..0..0..1
%K A259250 nonn,tabl
%O A259250 1,1
%A A259250 _R. H. Hardin_, Jun 22 2015