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A208287 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A208287 #7 Jul 22 2025 21:16:21
%S A208287 2,4,4,6,16,6,10,36,36,8,16,100,102,64,10,26,256,378,216,100,12,42,
%T A208287 676,1260,984,390,144,14,68,1764,4374,3984,2090,636,196,16,110,4624,
%U A208287 14946,16872,9900,3900,966,256,18,178,12100,51384,70216,49130,21096,6650,1392
%N A208287 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A208287 Table starts
%C A208287 ..2...4....6....10....16.....26......42.......68.......110........178
%C A208287 ..4..16...36...100...256....676....1764.....4624.....12100......31684
%C A208287 ..6..36..102...378..1260...4374...14946....51384....176238.....605022
%C A208287 ..8..64..216...984..3984..16872...70216...294192...1229400....5142728
%C A208287 .10.100..390..2090..9900..49130..239490..1175440...5754050...28195750
%C A208287 .12.144..636..3900.21096.119580..665892..3733080..20874900..116842500
%C A208287 .14.196..966..6650.40376.256774.1604862.10095932..63357434..397965218
%C A208287 .16.256.1392.10608.71360.502416.3478160.24229696.168399632.1171405168
%H A208287 R. H. Hardin, <a href="/A208287/b208287.txt">Table of n, a(n) for n = 1..1106</a>
%F A208287 Empirical for column k:
%F A208287 k=1: a(n) = 2*n
%F A208287 k=2: a(n) = 4*n^2
%F A208287 k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
%F A208287 k=4: a(n) = (4/3)*n^4 + 10*n^3 + (2/3)*n^2 - 2*n
%F A208287 k=5: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2
%F A208287 k=6: a(n) = (8/15)*n^6 + (23/3)*n^5 + (82/3)*n^4 + (1/3)*n^3 - (178/15)*n^2 + 2*n
%F A208287 k=7: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n
%e A208287 Some solutions for n=4 k=3
%e A208287 ..0..1..0....1..1..1....1..0..0....0..1..0....1..1..1....1..0..0....0..1..1
%e A208287 ..1..0..1....1..1..0....0..1..0....0..1..1....1..0..1....0..1..1....1..1..0
%e A208287 ..1..1..1....1..1..0....1..0..0....0..1..1....1..1..1....0..1..0....1..1..1
%e A208287 ..1..1..1....1..1..0....0..1..0....0..1..1....1..1..1....0..1..1....1..1..0
%Y A208287 Column 2 is A016742
%Y A208287 Column 3 is A086113
%Y A208287 Row 1 is A006355(n+2)
%Y A208287 Row 2 is A206981
%Y A208287 Row 3 is A060521
%K A208287 nonn,tabl
%O A208287 1,1
%A A208287 _R. H. Hardin_ Feb 25 2012