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A202444 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals. 1

%I

%S 484,836,1722,3122,5512,8996,14338,21674,32120,45844,64378,87922,

%T 118488,156308,203938,261642,332584,417060,518906,638450,780264,

%U 944708,1137154,1357994,1613464,1903988,2236730,2612146,3038392,3515956,4054050,4653194

%N Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

%C Column 5 of A202447.

%H R. H. Hardin, <a href="/A202444/b202444.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9) for n>10.

%F Empirical g.f.: 2*x*(242 - 308*x - 393*x^2 + 914*x^3 - 35*x^4 - 842*x^5 + 425*x^6 + 190*x^7 - 207*x^8 + 46*x^9) / ((1 - x)^6*(1 + x)^3). - _Colin Barker_, May 31 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A202447.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011

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Last modified January 24 10:01 EST 2022. Contains 350534 sequences. (Running on oeis4.)