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

1,1

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

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!

Example

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

Crossrefs

Sequence in context: A339983 A275996 A235292 * A202195 A242867 A255091

Adjacent sequences: A202199 A202200 A202201 * A202203 A202204 A202205

Keyword

nonn,tabl

Author

R. H. Hardin Dec 14 2011

Status

approved