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A208780 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 1 vertically.

%I A208780 #7 Jul 22 2025 21:29:54
%S A208780 2,4,4,6,16,6,10,36,36,10,16,100,36,100,16,26,256,60,60,256,26,42,676,
%T A208780 96,100,96,676,42,68,1764,156,160,160,156,1764,68,110,4624,252,260,
%U A208780 256,260,252,4624,110,178,12100,408,420,416,416,420,408,12100,178,288,31684,660
%N A208780 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 1 vertically.
%C A208780 Table starts
%C A208780 ..2....4...6..10...16...26...42...68...110...178...288....466....754....1220
%C A208780 ..4...16..36.100..256..676.1764.4624.12100.31684.82944.217156.568516.1488400
%C A208780 ..6...36..36..60...96..156..252..408...660..1068..1728...2796...4524....7320
%C A208780 .10..100..60.100..160..260..420..680..1100..1780..2880...4660...7540...12200
%C A208780 .16..256..96.160..256..416..672.1088..1760..2848..4608...7456..12064...19520
%C A208780 .26..676.156.260..416..676.1092.1768..2860..4628..7488..12116..19604...31720
%C A208780 .42.1764.252.420..672.1092.1764.2856..4620..7476.12096..19572..31668...51240
%C A208780 .68.4624.408.680.1088.1768.2856.4624..7480.12104.19584..31688..51272...82960
%H A208780 R. H. Hardin, <a href="/A208780/b208780.txt">Table of n, a(n) for n = 1..10018</a>
%F A208780 Empirical for column k:
%F A208780 k=1: a(n) = a(n-1) +a(n-2)
%F A208780 k=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F A208780 k=3: a(n) = a(n-1) +a(n-2) for n>4
%F A208780 k=4: a(n) = a(n-1) +a(n-2) for n>4
%F A208780 k=5: a(n) = a(n-1) +a(n-2) for n>4
%F A208780 k=6: a(n) = a(n-1) +a(n-2) for n>4
%F A208780 k=7: a(n) = a(n-1) +a(n-2) for n>4
%e A208780 Some solutions for n=4 k=3
%e A208780 ..1..0..0....0..1..1....1..1..0....0..1..0....0..1..1....0..1..0....0..1..1
%e A208780 ..1..0..1....0..1..0....1..0..0....1..0..0....0..1..1....0..1..1....1..0..1
%e A208780 ..0..1..0....1..0..1....0..1..0....0..1..1....1..0..0....1..0..0....0..1..0
%e A208780 ..1..0..1....0..1..0....1..0..1....1..0..0....0..1..1....0..1..0....1..0..0
%Y A208780 Column 1 is A006355(n+2)
%Y A208780 Column 2 is A206981
%Y A208780 Diagonal is A206981 and column 2 for n>1
%Y A208780 Column 3 is A022346(n+1) for n>2
%Y A208780 Column 4 is A022354(n+1) for n>2
%Y A208780 Column 5 is A022366(n+1) for n>2
%K A208780 nonn,tabl
%O A208780 1,1
%A A208780 _R. H. Hardin_ Mar 01 2012