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 A188516 Number of nX2 binary arrays without the pattern 1 1 0 diagonally, vertically or horizontally 16
 4, 16, 49, 144, 400, 1089, 2916, 7744, 20449, 53824, 141376, 370881, 972196, 2547216, 6671889, 17472400, 45751696, 119793025, 313644100, 821166336, 2149898689, 5628600576, 14736017664, 38579637889, 101003196100, 264430435984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 2 of A188523 LINKS R. H. Hardin, Table of n, a(n) for n = 1..200 FORMULA Empirical: a(n)=4*a(n-1)-2*a(n-2)-6*a(n-3)+4*a(n-4)+2*a(n-5)-a(n-6). Conjecture:  a(n) = (F(n)+3) - 1)^2, where F = A000045 (Fibonacci numbers). - Clark Kimberling, Jun 21 2016 Assuming the conjecture, define b(1) = 1 and b(n) = a(n-1) for n > 1.   Then b(n) = Sum{F(i,j): (i=n and 1<=j<=n) or (j=n and 1<=i<=n)}, where F is the Fibonacci fusion array, A202453. - Clark Kimberling, Jun 21 2016 G.f. for (b(n)):  -x*(-1+x^3-2*x^2) / ( (x-1)*(1+x)*(x^2-3*x+1)*(x^2+x-1) ). - R. J. Mathar, Dec 20 2011 b(n) = -2*(-1)^n/5 - 2*Fibonacci(n+2) + Lucas(2*n+4)/5 + 1. - Ehren Metcalfe, Mar 26 2016 EXAMPLE Some solutions for 3X2 ..0..1....0..1....0..0....0..0....1..0....0..1....1..0....0..1....0..0....0..1 ..0..0....0..0....0..0....0..1....1..1....1..0....0..1....0..1....1..0....1..0 ..1..1....0..0....0..1....1..0....1..1....0..0....1..0....1..1....0..0....0..1 CROSSREFS Sequence in context: A224147 A227266 A114185 * A188501 A283692 A173712 Adjacent sequences:  A188513 A188514 A188515 * A188517 A188518 A188519 KEYWORD nonn AUTHOR R. H. Hardin, Apr 02 2011 STATUS approved

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Last modified July 6 02:58 EDT 2022. Contains 355108 sequences. (Running on oeis4.)