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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. 9
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified May 28 19:08 EDT 2023. Contains 363019 sequences. (Running on oeis4.)