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A220304 Majority value maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal, vertical and antidiagonal neighbors in a random 0..1 n X 2 array. 1

%I #8 Jul 31 2018 08:53:20

%S 2,7,26,86,291,980,3309,11161,37656,127036,428581,1445887,4877950,

%T 16456589,55519107,187303144,631899019,2131818803,7192053308,

%U 24263615009,81857431864,276159968238,931672620616,3143156039330,10603971469191

%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, vertical and antidiagonal neighbors in a random 0..1 n X 2 array.

%C Column 2 of A220308.

%H R. H. Hardin, <a href="/A220304/b220304.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - a(n-3) + 6*a(n-4) + 3*a(n-6) + 3*a(n-7) - a(n-8) + 3*a(n-9) - a(n-10).

%F Empirical g.f.: x*(2 + x + 3*x^2 + 3*x^3 + 2*x^4 + 5*x^5 + 2*x^6 + 2*x^7 + x^8 + x^9) / (1 - 3*x - x^2 + x^3 - 6*x^4 - 3*x^6 - 3*x^7 + x^8 - 3*x^9 + x^10). - _Colin Barker_, Jul 31 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A220308.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2012

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)