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A202049 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns. 1

%I #9 May 26 2018 03:34:53

%S 966,3304,9170,22092,47950,95984,180054,320180,544390,890904,1410682,

%T 2170364,3255630,4775008,6864158,9690660,13459334,18418120,24864546,

%U 33152812,43701518,57002064,73627750,94243604,119616966,150628856

%N Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns.

%C Column 5 of A202052.

%H R. H. Hardin, <a href="/A202049/b202049.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/180)*n^7 + (7/36)*n^6 + (511/180)*n^5 + (805/36)*n^4 + (4606/45)*n^3 + (2443/9)*n^2 + (1854/5)*n + 196.

%F Conjectures from _Colin Barker_, May 26 2018: (Start)

%F G.f.: 14*x*(69 - 316*x + 699*x^2 - 918*x^3 + 755*x^4 - 384*x^5 + 111*x^6 - 14*x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A202052.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2011

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Last modified July 22 10:58 EDT 2024. Contains 374490 sequences. (Running on oeis4.)