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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..2 2Xn array
1

%I #4 Dec 25 2012 06:35:18

%S 1,10,44,163,626,2351,8950,33895,128696,488096,1852077,7026179,

%T 26657630,101135949,383705313,1455749117,5523022944,20953977348,

%U 79498036036,301610318916,1144289865773,4341360811888,16470839047751,62489285631772

%N 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..2 2Xn array

%C Row 2 of A220922

%H R. H. Hardin, <a href="/A220923/b220923.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +3*a(n-2) -16*a(n-3) +3*a(n-4) +17*a(n-5) -16*a(n-6) -8*a(n-7) +12*a(n-8) -12*a(n-9) +8*a(n-10) -8*a(n-12) +16*a(n-13) -16*a(n-14) -32*a(n-15)

%e Some solutions for n=3

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 25 2012