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A258316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 or 0011.

%I A258316 #19 Jun 02 2025 11:47:37
%S A258316 5,7,7,10,9,10,15,12,12,15,23,17,15,17,23,36,25,20,20,25,36,57,38,28,
%T A258316 25,28,38,57,91,59,41,33,33,41,59,91,146,93,62,46,41,46,62,93,146,235,
%U A258316 148,96,67,54,54,67,96,148,235,379,237,151,101,75,67,75,101,151,237,379,612
%N A258316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 or 0011.
%C A258316 Table starts
%C A258316 ...5...7..10..15..23..36..57..91.146.235.379.612..989.1599.2586.4183.6767.10948
%C A258316 ...7...9..12..17..25..38..59..93.148.237.381.614..991.1601.2588.4185.6769.10950
%C A258316 ..10..12..15..20..28..41..62..96.151.240.384.617..994.1604.2591.4188.6772.10953
%C A258316 ..15..17..20..25..33..46..67.101.156.245.389.622..999.1609.2596.4193.6777.10958
%C A258316 ..23..25..28..33..41..54..75.109.164.253.397.630.1007.1617.2604.4201.6785.10966
%C A258316 ..36..38..41..46..54..67..88.122.177.266.410.643.1020.1630.2617.4214.6798.10979
%C A258316 ..57..59..62..67..75..88.109.143.198.287.431.664.1041.1651.2638.4235.6819.11000
%C A258316 ..91..93..96.101.109.122.143.177.232.321.465.698.1075.1685.2672.4269.6853.11034
%C A258316 .146.148.151.156.164.177.198.232.287.376.520.753.1130.1740.2727.4324.6908.11089
%C A258316 .235.237.240.245.253.266.287.321.376.465.609.842.1219.1829.2816.4413.6997.11178
%C A258316 Apparently: put 1s in some number of nonadjacent columns or put 1s in some number of nonadjacent rows
%H A258316 R. H. Hardin, <a href="/A258316/b258316.txt">Table of n, a(n) for n = 1..1104</a>
%F A258316 Empirical: T(n,k) = Fibonacci(n+3) +Fibonacci(k+3) -1
%F A258316 Empirical for rows, columns and nw-se diagonals: a(n) = 2*a(n-1) -a(n-3)
%e A258316 Some solutions for n=4 k=4
%e A258316 ..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1
%e A258316 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A258316 ..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%e A258316 ..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e A258316 ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%Y A258316 Column 1 is A018910
%Y A258316 Column 2 is A157727(n+3)
%Y A258316 Column 3 is A187107(n+3)
%Y A258316 Diagonal is A001595(n+2)
%Y A258316 Superdiagonal 1 is A000071(n+5)
%Y A258316 Superdiagonal 2 is A001610(n+3)
%Y A258316 Superdiagonal 3 is A001595(n+4)
%Y A258316 Superdiagonal 5 is A022308(n+5)
%Y A258316 Superdiagonal 6 is A022319(n+5)
%Y A258316 Superdiagonal 7 is A022407(n+5)
%Y A258316 Superdiagonal 9 is A022323(n+7)
%K A258316 nonn,tabl
%O A258316 1,1
%A A258316 _R. H. Hardin_, Jun 29 2015