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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 and antidiagonal neighbors in a random 0..2 2 X n array.
2

%I #6 May 09 2022 00:35:44

%S 1,7,33,119,457,1710,6466,24433,92196,347977,1313608,4958107,18714962,

%T 70641589,266642543,1006466983,3799003546,14339684590,54126460553,

%U 204305303067,771169136489,2910848804238,10987266400303,41472446978323

%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 and antidiagonal neighbors in a random 0..2 2 X n array.

%C Row 2 of A221035.

%H R. H. Hardin, <a href="/A221036/b221036.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) -12*a(n-4) -2*a(n-5) +22*a(n-6) -20*a(n-7) +16*a(n-8) +8*a(n-9) -6*a(n-10) -10*a(n-11) +a(n-12) +2*a(n-13) -2*a(n-14) +2*a(n-15) for n>19.

%e Some solutions for n=3

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

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

%Y Cf. A221035.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 29 2012