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A208688 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

%I A208688 #7 Jul 22 2025 21:27:55
%S A208688 2,4,4,6,16,6,10,36,36,9,16,100,78,81,14,26,256,282,189,196,21,42,676,
%T A208688 768,927,490,441,31,68,1764,2430,2889,3430,1113,961,46,110,4624,7086,
%U A208688 11727,12096,11067,2449,2116,68,178,12100,21588,40581,66094,41013,34627
%N A208688 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.
%C A208688 Table starts
%C A208688 ..2....4....6.....10.....16......26.......42........68........110.........178
%C A208688 ..4...16...36....100....256.....676.....1764......4624......12100.......31684
%C A208688 ..6...36...78....282....768....2430.....7086.....21588......64230......193554
%C A208688 ..9...81..189....927...2889...11727....40581....154359.....554733.....2062215
%C A208688 .14..196..490...3430..12096...66094...269766...1331988....5795314....27403166
%C A208688 .21..441.1113..11067..41013..301035..1346961...8556723...42184905...249260739
%C A208688 .31..961.2449..34627.133207.1332721..6398617..53340739..290904031..2188890625
%C A208688 .46.2116.5474.111642.444912.6219706.31733422.358035204.2130519946.21086588370
%H A208688 R. H. Hardin, <a href="/A208688/b208688.txt">Table of n, a(n) for n = 1..1360</a>
%F A208688 Empirical for row n:
%F A208688 n=1: a(k)=a(k-1)+a(k-2)
%F A208688 n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)
%F A208688 n=3: a(k)=2*a(k-1)+4*a(k-2)-3*a(k-3)
%F A208688 n=4: a(k)=a(k-1)+10*a(k-2)+2*a(k-3)-10*a(k-4)
%F A208688 n=5: a(k)=a(k-1)+17*a(k-2)+4*a(k-3)-32*a(k-4)
%F A208688 n=6: a(k)=a(k-1)+26*a(k-2)+6*a(k-3)-78*a(k-4)
%F A208688 n=7: a(k)=a(k-1)+39*a(k-2)+9*a(k-3)-180*a(k-4)
%e A208688 Some solutions for n=4 k=3
%e A208688 ..1..1..0....0..1..1....0..1..1....0..1..0....0..1..1....1..1..1....1..0..1
%e A208688 ..0..1..0....0..1..1....0..1..0....0..1..0....0..1..1....1..1..1....1..1..0
%e A208688 ..0..1..0....0..1..1....1..1..0....0..1..1....1..1..0....1..1..1....1..0..0
%e A208688 ..1..1..0....0..1..1....0..1..1....1..1..0....0..1..0....0..1..0....1..0..1
%Y A208688 Column 1 is A038718(n+2)
%Y A208688 Column 2 is A207069
%Y A208688 Column 3 is A207724
%Y A208688 Row 1 is A006355(n+2)
%Y A208688 Row 2 is A206981
%K A208688 nonn,tabl
%O A208688 1,1
%A A208688 _R. H. Hardin_ Mar 01 2012