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A181245 T(n,k)=Number of nXk binary matrices with no 2X2 circuit having pattern 0101 in any orientation 9

%I

%S 2,4,4,8,14,8,16,50,50,16,32,178,322,178,32,64,634,2066,2066,634,64,

%T 128,2258,13262,23858,13262,2258,128,256,8042,85126,275690,275690,

%U 85126,8042,256,512,28642,546410,3185462,5735478,3185462,546410,28642,512,1024

%N T(n,k)=Number of nXk binary matrices with no 2X2 circuit having pattern 0101 in any orientation

%C Table starts

%C ....2......4.........8..........16.............32...............64

%C ....4.....14........50.........178............634.............2258

%C ....8.....50.......322........2066..........13262............85126

%C ...16....178......2066.......23858.........275690..........3185462

%C ...32....634.....13262......275690........5735478........119310334

%C ...64...2258.....85126.....3185462......119310334.......4468252414

%C ..128...8042....546410....36806846.....2481942354.....167341334542

%C ..256..28642...3507314...425288998....51630303190....6267120468434

%C ..512.102010..22512862..4914052362..1074033301458..234710735573170

%C .1024.363314.144506294.56780001474.22342450688162.8790181730741270

%H R. H. Hardin, <a href="/A181245/b181245.txt">Table of n, a(n) for n=1..480</a>

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

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

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

%F 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)

%F 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)

%F 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)

%F 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)

%e All solutions for 2X2

%e ..0..0....0..0....0..0....0..0....0..1....0..1....0..1....1..0....1..0....1..0

%e ..0..0....0..1....1..0....1..1....0..0....0..1....1..1....0..0....1..0....1..1

%e ...

%e ..1..1....1..1....1..1....1..1

%e ..0..0....0..1....1..0....1..1

%Y Diagonal is A133130(n-1)

%Y Column 2 is A055099

%Y Column 3 is A133129

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Oct 10 2010

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)