A202202 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 101 in rows and columns.

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

Offset: 1

Author

R. H. Hardin Dec 14 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..839

Formula

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!