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Number of 2 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).
1

%I #9 Oct 01 2018 09:28:17

%S 3,8,34,144,612,2613,11159,47675,203696,870316,3718550,15888022,

%T 67883780,290042861,1239248291,5294859950,22623022401,96659996189,

%U 412993219856,1764570725956,7539372796546,32213014377497,137634565007885

%N Number of 2 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

%H R. H. Hardin, <a href="/A231856/b231856.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 5*a(n-3) - a(n-4) + 10*a(n-5) - 3*a(n-6) - 3*a(n-7) + a(n-8) for n>9.

%F Empirical g.f.: x*(3 - 7*x + 5*x^3 + 3*x^4 - 11*x^5 + x^6 + 3*x^7 - x^8) / ((1 + x - x^3)*(1 - 6*x + 8*x^2 - 2*x^3 - 3*x^4 + x^5)). - _Colin Barker_, Oct 01 2018

%e Some solutions for n=7:

%e ..0..0..0..2..2..2..2....0..2..2..2..2..0..2....0..2..2..1..1..2..2

%e ..1..1..2..2..2..0..1....2..2..2..2..1..1..1....1..1..1..1..0..0..0

%Y Row 2 of A231855.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2013