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Majority value maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 2 X n array.
1

%I #7 Jul 31 2018 07:22:43

%S 1,6,18,51,157,477,1445,4384,13297,40332,122339,371085,1125588,

%T 3414184,10356065,31412486,95281776,289013030,876647491,2659087097,

%U 8065664119,24465139829,74208776604,225093441705,682763681270,2070989900565

%N Majority value maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 2 X n array.

%C Row 2 of A220226.

%H R. H. Hardin, <a href="/A220227/b220227.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + 6*a(n-3) + a(n-4) + 3*a(n-5) - 4*a(n-6) - 2*a(n-7) - 4*a(n-8).

%F Empirical g.f.: x*(1 - x)*(1 + 2*x)^2*(1 + x^2)*(1 + x + x^2) / (1 - 2*x - x^2 - 6*x^3 - x^4 - 3*x^5 + 4*x^6 + 2*x^7 + 4*x^8). - _Colin Barker_, Jul 31 2018

%e Some solutions for n=3:

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

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

%Y Cf. A220226.

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 08 2012