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A207068 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207068 #7 Jul 22 2025 19:59:40
%S A207068 2,4,4,6,16,6,9,36,36,8,14,81,102,64,10,21,196,288,216,100,12,31,441,
%T A207068 896,720,390,144,14,46,961,2499,2688,1485,636,196,16,68,2116,6634,
%U A207068 8799,6398,2709,966,256,18,100,4624,17848,27063,23856,13132,4536,1392,324,20,147
%N A207068 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207068 Table starts
%C A207068 ..2...4....6....9....14.....21.....31......46.......68......100.......147
%C A207068 ..4..16...36...81...196....441....961....2116.....4624....10000.....21609
%C A207068 ..6..36..102..288...896...2499...6634...17848....47192...122200....315315
%C A207068 ..8..64..216..720..2688...8799..27063...84502...257584...762900...2246895
%C A207068 .10.100..390.1485..6398..23856..82739..291364...997288..3297100..10818024
%C A207068 .12.144..636.2709.13132..54684.210118..818892..3093184.11234900..40417797
%C A207068 .14.196..966.4536.24304.111426.468348.1992996..8204200.32364700.126207438
%C A207068 .16.256.1392.7128.41664.208026.947298.4356936.19360144.82226100.344542569
%H A207068 R. H. Hardin, <a href="/A207068/b207068.txt">Table of n, a(n) for n = 1..1404</a>
%F A207068 Empirical for column k:
%F A207068 k=1: a(n) = 2*n
%F A207068 k=2: a(n) = 4*n^2
%F A207068 k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
%F A207068 k=4: a(n) = (3/4)*n^4 + (15/2)*n^3 + (15/4)*n^2 - 3*n
%F A207068 k=5: a(n) = (7/30)*n^5 + 7*n^4 + (21/2)*n^3 - (56/15)*n
%F A207068 k=6: a(n) = (7/120)*n^6 + (147/40)*n^5 + (49/3)*n^4 + (91/8)*n^3 - (707/120)*n^2 - (91/20)*n
%F A207068 k=7: a(n) = (31/2520)*n^7 + (62/45)*n^6 + (4867/360)*n^5 + (2015/72)*n^4 + (1271/180)*n^3 - (4991/360)*n^2 - (713/140)*n
%e A207068 Some solutions for n=4 k=3
%e A207068 ..0..1..1....1..1..1....0..1..1....0..0..0....0..1..1....0..0..0....1..0..0
%e A207068 ..1..1..0....1..1..0....1..0..0....1..0..0....0..1..1....0..1..1....0..0..0
%e A207068 ..1..1..0....1..0..0....1..0..0....0..0..0....0..1..1....0..0..0....0..0..0
%e A207068 ..1..0..0....1..0..0....1..0..0....0..0..0....0..1..1....0..0..0....0..0..0
%Y A207068 Column 2 is A016742
%Y A207068 Column 3 is A086113
%Y A207068 Row 1 is A038718(n+2)
%K A207068 nonn,tabl
%O A207068 1,1
%A A207068 _R. H. Hardin_ Feb 14 2012