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A208379 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A208379 #7 Jul 22 2025 21:18:49
%S A208379 2,4,4,6,16,6,10,36,36,8,16,100,72,64,10,26,256,240,108,100,12,42,676,
%T A208379 704,420,144,144,14,68,1764,2080,1344,640,180,196,16,110,4624,6216,
%U A208379 4212,2176,900,216,256,18,178,12100,18496,13860,7072,3200,1200,252,324,20,288
%N A208379 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A208379 Table starts
%C A208379 ..2...4...6...10...16....26....42.....68.....110.....178......288......466
%C A208379 ..4..16..36..100..256...676..1764...4624...12100...31684....82944...217156
%C A208379 ..6..36..72..240..704..2080..6216..18496...55000..163760...487296..1450192
%C A208379 ..8..64.108..420.1344..4212.13860..44880..144540..468852..1517184..4906980
%C A208379 .10.100.144..640.2176..7072.25200..87040..296560.1028128..3545856.12198016
%C A208379 .12.144.180..900.3200.10660.40740.148240..526900.1931300..7015680.25336420
%C A208379 .14.196.216.1200.4416.14976.60984.231744..851400.3276624.12438144.46737936
%C A208379 .16.256.252.1540.5824.20020.86436.340816.1285900.5170900.20393856.79220932
%H A208379 R. H. Hardin, <a href="/A208379/b208379.txt">Table of n, a(n) for n = 1..1463</a>
%F A208379 Empirical for column k:
%F A208379 k=1: a(n) = 2*n
%F A208379 k=2: a(n) = 4*n^2
%F A208379 k=3: a(n) = 36*n - 36 for n>1
%F A208379 k=4: a(n) = 20*n^2 + 40*n - 60 for n>1
%F A208379 k=5: a(n) = 96*n^2 - 32*n - 64 for n>1
%F A208379 k=6: a(n) = 364*n^2 - 416*n + 52 for n>1
%F A208379 k=7: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1
%F A208379 Empirical for row n:
%F A208379 n=1: a(k)=a(k-1)+a(k-2)
%F A208379 n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)
%F A208379 n=3: a(k)=a(k-1)+4*a(k-2)+5*a(k-3)+2*a(k-4)-a(k-5)+a(k-6) for k>8
%F A208379 n=4: a(k)=a(k-1)+4*a(k-2)+9*a(k-3)+5*a(k-4)-2*a(k-5)+4*a(k-6) for k>8
%F A208379 n=5: a(k)=a(k-1)+4*a(k-2)+13*a(k-3)+8*a(k-4)-3*a(k-5)+9*a(k-6) for k>8
%F A208379 n=6: a(k)=a(k-1)+4*a(k-2)+17*a(k-3)+11*a(k-4)-4*a(k-5)+16*a(k-6) for k>8
%F A208379 n=7: a(k)=a(k-1)+4*a(k-2)+21*a(k-3)+14*a(k-4)-5*a(k-5)+25*a(k-6) for k>8
%e A208379 Some solutions for n=4 k=3
%e A208379 ..0..1..0....0..1..1....1..1..0....0..0..1....0..0..1....1..0..1....1..0..0
%e A208379 ..1..1..0....0..1..1....1..1..0....0..1..1....1..0..1....1..1..0....1..0..0
%e A208379 ..1..1..0....0..0..1....1..1..0....0..1..0....0..0..1....0..1..0....1..0..0
%e A208379 ..1..0..0....0..0..1....1..1..0....0..1..0....0..0..1....0..1..0....1..0..0
%Y A208379 Column 1 is A004275(n+1)
%Y A208379 Column 2 is A016742
%Y A208379 Column 3 is A044102(n-1) for n>1
%Y A208379 Row 1 is A006355(n+2)
%Y A208379 Row 2 is A206981
%Y A208379 Row 3 is A207840
%K A208379 nonn,tabl
%O A208379 1,1
%A A208379 _R. H. Hardin_ Feb 25 2012