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proposed

Majority value maps: number of 2 X 2Xnn 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 2Xnn array.

Row 2 of A220226.

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)).

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

Some solutions for n=3:

Cf. A220226.

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

allocated for R. H. Hardin

Majority value maps: number of 2Xn 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 2Xn array

1, 6, 18, 51, 157, 477, 1445, 4384, 13297, 40332, 122339, 371085, 1125588, 3414184, 10356065, 31412486, 95281776, 289013030, 876647491, 2659087097, 8065664119, 24465139829, 74208776604, 225093441705, 682763681270, 2070989900565

1,2

Row 2 of A220226

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)

Some solutions for n=3

..1..1..0....1..1..1....1..0..0....1..0..1....0..1..0....0..1..1....1..1..1

..1..1..0....1..0..1....0..0..0....1..1..1....1..1..1....0..1..1....0..1..0

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nonn

R. H. Hardin Dec 08 2012

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allocated for R. H. Hardin

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