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A202202
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T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 101 in rows and columns
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9
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108, 240, 240, 450, 640, 450, 756, 1400, 1400, 756, 1176, 2688, 3500, 2688, 1176, 1728, 4704, 7560, 7560, 4704, 1728, 2430, 7680, 14700, 18144, 14700, 7680, 2430, 3300, 11880, 26400, 38808, 38808, 26400, 11880, 3300, 4356, 17600, 44550, 76032, 90552
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OFFSET
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1,1
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COMMENTS
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Table starts
..108...240....450....756....1176....1728.....2430.....3300.....4356......5616
..240...640...1400...2688....4704....7680....11880....17600....25168.....34944
..450..1400...3500...7560...14700...26400....44550....71500...110110....163800
..756..2688...7560..18144...38808...76032...138996...240240...396396....628992
.1176..4704..14700..38808...90552..192192...378378...700700..1233232...2079168
.1728..7680..26400..76032..192192..439296...926640..1830400..3422848...6110208
.2430.11880..44550.138996..378378..926640..2084940..4375800..8664084..16325712
.3300.17600..71500.240240..700700.1830400..4375800..9724000.20323160..40310400
.4356.25168.110110.396396.1233232.3422848..8664084.20323160.44710952..93117024
.5616.34944.163800.628992.2079168.6110208.16325712.40310400.93117024.203164416
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LINKS
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FORMULA
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Empirical: column k is a polynomial of degree k+2
(via factored column polynomials) T(n,k)=2*(k+2)*(n+2)*product{i=2..k+2 : (n+i) } / n!
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EXAMPLE
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Some solutions for n=4 k=3
..0..1..1..1..1....1..1..0..0..0....0..1..0..0..0....0..1..1..1..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..0....1..1..1..0..0
..1..1..0..0..0....1..1..1..1..1....1..1..1..0..0....0..0..0..0..0
..1..1..0..0..0....1..1..1..1..1....1..1..1..0..0....0..0..0..0..0
..0..1..0..0..0....1..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..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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