A181245 T(n,k) = Number of n X k binary matrices with no 2 X 2 circuit having pattern 0101 in any orientation.

2, 4, 4, 8, 14, 8, 16, 50, 50, 16, 32, 178, 322, 178, 32, 64, 634, 2066, 2066, 634, 64, 128, 2258, 13262, 23858, 13262, 2258, 128, 256, 8042, 85126, 275690, 275690, 85126, 8042, 256, 512, 28642, 546410, 3185462, 5735478, 3185462, 546410, 28642, 512, 1024

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn
• tabl

Comments

Table starts

....2......4.........8..........16.............32...............64

....4.....14........50.........178............634.............2258

....8.....50.......322........2066..........13262............85126

...16....178......2066.......23858.........275690..........3185462

...32....634.....13262......275690........5735478........119310334

...64...2258.....85126.....3185462......119310334.......4468252414

..128...8042....546410....36806846.....2481942354.....167341334542

..256..28642...3507314...425288998....51630303190....6267120468434

..512.102010..22512862..4914052362..1074033301458..234710735573170

.1024.363314.144506294.56780001474.22342450688162.8790181730741270

Examples

			All solutions for 2X2
..0..0....0..0....0..0....0..0....0..1....0..1....0..1....1..0....1..0....1..0
..0..0....0..1....1..0....1..1....0..0....0..1....1..1....0..0....1..0....1..1
...
..1..1....1..1....1..1....1..1
..0..0....0..1....1..0....1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..480

Crossrefs

Main diagonal is A133130.

Column 2 is A055099.

Column 3 is A133129.

Formula

Empirical column 1: a(n)=2*a(n-1)

Empirical column 2: a(n)=3*a(n-1)+2*a(n-2)

Empirical column 3: a(n)=6*a(n-1)+3*a(n-2)-2*a(n-3)

Empirical column 4: a(n)=10*a(n-1)+20*a(n-2)-21*a(n-3)-30*a(n-4)+8*a(n-5)

Empirical column 5: a(n)=21*a(n-1)+9*a(n-2)-278*a(n-3)+73*a(n-4)+790*a(n-5)-662*a(n-6)+29*a(n-7)+69*a(n-8)-10*a(n-9)

Empirical column 6: a(n)=36*a(n-1)+120*a(n-2)-2391*a(n-3)-3905*a(n-4)+50702*a(n-5)+27152*a(n-6)-396016*a(n-7)+154999*a(n-8)+751787*a(n-9)-499260*a(n-10)-410368*a(n-11)+355981*a(n-12)+38077*a(n-13)-70276*a(n-14)+6203*a(n-15)+3386*a(n-16)-622*a(n-17)+28*a(n-18)

Empirical column 7: a(n)=77*a(n-1)-429*a(n-2)-16791*a(n-3)+132938*a(n-4)+1140609*a(n-5)-11250708*a(n-6)-21101443*a(n-7)[phone]*a(n-8)-276630106*a(n-9)-3595865197*a(n-10)[phone]*a(n-11)[phone]*a(n-12)-30419637636*a(n-13)-37486637674*a(n-14)[phone]*a(n-15)[phone]*a(n-16)-140235056122*a(n-17)-7589163210*a(n-18)[phone]*a(n-19)-23221600421*a(n-20)-65939015129*a(n-21)[phone]*a(n-22)[phone]*a(n-23)-8259596531*a(n-24)-2431120428*a(n-25)[phone]*a(n-26)[phone]*a(n-27)-123174410*a(n-28)+8581030*a(n-29)+3300116*a(n-30)-512304*a(n-31)+18304*a(n-32)