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A202050 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns. 1

%I #11 May 26 2018 08:45:33

%S 1392,5216,15760,41088,95984,205792,411696,777760,1400080,2418432,

%T 4030832,6511456,10232400,15689792,23534800,34610112,49992496,

%U 71042080,99459024,137348288,187293232,252438816,336585200,444292576,580998096

%N Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.

%C Column 6 of A202052.

%H R. H. Hardin, <a href="/A202050/b202050.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/1260)*n^8 + (11/315)*n^7 + (59/90)*n^6 + (308/45)*n^5 + (7807/180)*n^4 + (7667/45)*n^3 + (14139/35)*n^2 + (17876/35)*n + 256.

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

%F G.f.: 16*x*(87 - 457*x + 1183*x^2 - 1869*x^3 + 1925*x^4 - 1307*x^5 + 567*x^6 - 143*x^7 + 16*x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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