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A207254 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

%I A207254 #7 Jul 22 2025 20:13:00
%S A207254 2,4,4,6,16,6,8,36,36,10,10,64,102,100,16,12,100,216,370,256,26,14,
%T A207254 144,390,940,1232,676,42,16,196,636,1950,3776,4238,1764,68,18,256,966,
%U A207254 3560,9072,15652,14406,4624,110,20,324,1392,5950,18688,43498,64176,49164
%N A207254 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
%C A207254 Table starts
%C A207254 ..2....4.....6......8.....10......12......14.......16.......18.......20
%C A207254 ..4...16....36.....64....100.....144.....196......256......324......400
%C A207254 ..6...36...102....216....390.....636.....966.....1392.....1926.....2580
%C A207254 .10..100...370....940...1950....3560....5950.....9320....13890....19900
%C A207254 .16..256..1232...3776...9072...18688...34608....59264....95568...146944
%C A207254 .26..676..4238..15652..43498..101036..207298...388232...677898..1119716
%C A207254 .42.1764.14406..64176.206514..541380.1231650..2524704..4777290..8483748
%C A207254 .68.4624.49164.263976.982940.2906592.7328836.16436824.33693660.64313720
%H A207254 R. H. Hardin, <a href="/A207254/b207254.txt">Table of n, a(n) for n = 1..1057</a>
%F A207254 Empirical for row n:
%F A207254 n=1: a(k) = 2*k
%F A207254 n=2: a(k) = 4*k^2
%F A207254 n=3: a(k) = 2*k^3 + 6*k^2 - 2*k
%F A207254 n=4: a(k) = (5/6)*k^4 + (35/3)*k^3 - (5/6)*k^2 - (5/3)*k
%F A207254 n=5: a(k) = (4/15)*k^5 + (32/3)*k^4 + (44/3)*k^3 - (32/3)*k^2 + (16/15)*k
%F A207254 n=6: a(k) = (13/180)*k^6 + (143/20)*k^5 + (1235/36)*k^4 - (39/4)*k^3 - (377/45)*k^2 + (13/5)*k
%F A207254 n=7: a(k) = (1/60)*k^7 + (77/20)*k^6 + (2527/60)*k^5 + (119/4)*k^4 - (644/15)*k^3 + (42/5)*k^2 + (4/5)*k
%e A207254 Some solutions for n=4 k=3
%e A207254 ..1..1..0....0..0..0....1..0..0....0..0..0....1..1..1....1..0..0....1..1..1
%e A207254 ..1..0..0....0..0..0....0..0..0....0..1..1....1..1..1....1..0..0....1..1..1
%e A207254 ..1..0..0....1..1..1....0..0..0....1..1..1....0..1..0....1..0..0....1..1..1
%e A207254 ..0..1..1....1..1..1....0..1..1....1..0..0....0..1..0....1..0..0....1..1..1
%Y A207254 Column 1 is A006355(n+2)
%Y A207254 Column 2 is A206981
%Y A207254 Row 2 is A016742
%Y A207254 Row 3 is A086113
%K A207254 nonn,tabl
%O A207254 1,1
%A A207254 _R. H. Hardin_ Feb 16 2012