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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
OFFSET
1,1
COMMENTS
Column 2 of A188523
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 02 2011
STATUS
approved