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A220255 Majority value maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and vertical neighbors in a random 0..2 n X 2 array. 4

%I

%S 2,10,35,132,497,1881,7102,26812,101196,381984,1441824,5442322,

%T 20542516,77539656,292680498,1104749538,4169978558,15739967580,

%U 59411954244,224255883112,846474444862,3195095604792,12060182066934,45522265840738

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

%C Column 2 of A220259.

%H R. H. Hardin, <a href="/A220255/b220255.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 4*a(n-2) - 4*a(n-3) - 3*a(n-6) - 2*a(n-7) + 2*a(n-8) + 2*a(n-9) for n>12.

%F Empirical g.f.: x*(2 + 4*x - 3*x^2 - 5*x^3 + x^4 + 2*x^5 + 5*x^6 + 4*x^7 - 3*x^8 - 2*x^9 + x^10 + x^11) / (1 - 3*x - 4*x^2 + 4*x^3 + 3*x^6 + 2*x^7 - 2*x^8 - 2*x^9). - _Colin Barker_, Feb 21 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A220259.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 08 2012

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Last modified August 10 11:57 EDT 2022. Contains 356039 sequences. (Running on oeis4.)