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A267644
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T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.
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8
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1, 2, 2, 3, 8, 3, 5, 18, 18, 5, 7, 50, 51, 50, 7, 11, 98, 189, 189, 98, 11, 15, 242, 429, 1015, 429, 242, 15, 23, 450, 1353, 2887, 2887, 1353, 450, 23, 31, 1058, 2829, 12623, 8917, 12623, 2829, 1058, 31, 47, 1922, 8427, 32303, 47715, 47715, 32303, 8427, 1922, 47, 63
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OFFSET
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1,2
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COMMENTS
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Table starts
..1....2.....3.......5.......7........11........15..........23..........31
..2....8....18......50......98.......242.......450........1058........1922
..3...18....51.....189.....429......1353......2829........8427.......16899
..5...50...189....1015....2887.....12623.....32303......131673......319541
..7...98...429....2887....8917.....47715....128441......647101.....1614281
.11..242..1353...12623...47715....343145...1117207.....7479533....22499181
.15..450..2829...32303..128441...1117207...3696933....30649693....90914453
.23.1058..8427..131673..647101...7479533..30649693...330654951..1225925501
.31.1922.16899..319541.1614281..22499181..90914453..1225925501..4301737251
.47.4418.49443.1277029.8168679.150415627.784186403.13431652713.62439362175
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
k=2: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -8*a(n-4) +8*a(n-5)
k=3: [order 11]
k=4: [order 35]
k=5: [order 93]
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1....0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..1
..0..0..1..0....1..0..1..0....1..0..1..1....1..1..0..0....1..0..1..0
..1..1..0..1....1..0..0..1....0..1..0..0....0..0..1..1....0..1..1..0
..1..0..0..1....0..1..1..0....1..0..1..0....0..1..0..0....1..0..0..1
..0..0..1..0....0..1..0..1....0..1..0..1....1..0..1..1....1..1..0..0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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