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

1,1

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

Links

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

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)+356560316*a(n-8)-276630106*a(n-9)-3595865197*a(n-10)+5253257444*a(n-11)+16399879057*a(n-12)-30419637636*a(n-13)-37486637674*a(n-14)+87632998667*a(n-15)+40083109062*a(n-16)-140235056122*a(n-17)-7589163210*a(n-18)+128111780723*a(n-19)-23221600421*a(n-20)-65939015129*a(n-21)+21868944788*a(n-22)+18307048178*a(n-23)-8259596531*a(n-24)-2431120428*a(n-25)+1497147381*a(n-26)+85285300*a(n-27)-123174410*a(n-28)+8581030*a(n-29)+3300116*a(n-30)-512304*a(n-31)+18304*a(n-32)

Example

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

Crossrefs

Diagonal is A133130(n-1).

Column 2 is A055099.

Column 3 is A133129.

Sequence in context: A047073 A308528 A069753 * A216950 A240364 A225982

Adjacent sequences: A181242 A181243 A181244 * A181246 A181247 A181248

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 10 2010

Status

approved