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

%I A181245 #7 May 21 2025 21:00:28
%S A181245 2,4,4,8,14,8,16,50,50,16,32,178,322,178,32,64,634,2066,2066,634,64,
%T A181245 128,2258,13262,23858,13262,2258,128,256,8042,85126,275690,275690,
%U A181245 85126,8042,256,512,28642,546410,3185462,5735478,3185462,546410,28642,512,1024
%N A181245 T(n,k) = Number of n X k binary matrices with no 2 X 2 circuit having pattern 0101 in any orientation.
%C A181245 Table starts
%C A181245 ....2......4.........8..........16.............32...............64
%C A181245 ....4.....14........50.........178............634.............2258
%C A181245 ....8.....50.......322........2066..........13262............85126
%C A181245 ...16....178......2066.......23858.........275690..........3185462
%C A181245 ...32....634.....13262......275690........5735478........119310334
%C A181245 ...64...2258.....85126.....3185462......119310334.......4468252414
%C A181245 ..128...8042....546410....36806846.....2481942354.....167341334542
%C A181245 ..256..28642...3507314...425288998....51630303190....6267120468434
%C A181245 ..512.102010..22512862..4914052362..1074033301458..234710735573170
%C A181245 .1024.363314.144506294.56780001474.22342450688162.8790181730741270
%H A181245 R. H. Hardin, <a href="/A181245/b181245.txt">Table of n, a(n) for n=1..480</a>
%F A181245 Empirical column 1: a(n)=2*a(n-1)
%F A181245 Empirical column 2: a(n)=3*a(n-1)+2*a(n-2)
%F A181245 Empirical column 3: a(n)=6*a(n-1)+3*a(n-2)-2*a(n-3)
%F A181245 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 A181245 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 A181245 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 A181245 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 A181245 All solutions for 2X2
%e A181245 ..0..0....0..0....0..0....0..0....0..1....0..1....0..1....1..0....1..0....1..0
%e A181245 ..0..0....0..1....1..0....1..1....0..0....0..1....1..1....0..0....1..0....1..1
%e A181245 ...
%e A181245 ..1..1....1..1....1..1....1..1
%e A181245 ..0..0....0..1....1..0....1..1
%Y A181245 Main diagonal is A133130.
%Y A181245 Column 2 is A055099.
%Y A181245 Column 3 is A133129.
%K A181245 nonn,tabl
%O A181245 1,1
%A A181245 _R. H. Hardin_, Oct 10 2010