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 A231636 Number of n X 2 0..2 arrays with no element having a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions). 1

%I #11 Sep 30 2018 02:44:41

%S 1,5,25,124,599,2907,14098,68345,331411,1606976,7792087,37783439,

%T 183209634,888373029,4307670407,20887647824,101283014043,491115562211,

%U 2381391364586,11547230982705,55991864805211,271501360719136

%N Number of n X 2 0..2 arrays with no element having a strict majority of its horizontal, vertical, diagonal 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="/A231636/b231636.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 11*a(n-2) + 4*a(n-3) - 14*a(n-4) + 48*a(n-5) - 48*a(n-6) + 16*a(n-7).

%F Empirical g.f.: x*(1 - x)^2 / (1 - 7*x + 11*x^2 - 4*x^3 + 14*x^4 - 48*x^5 + 48*x^6 - 16*x^7). - _Colin Barker_, Sep 29 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 2 of A231641.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 12 2013

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Last modified October 3 10:11 EDT 2023. Contains 365859 sequences. (Running on oeis4.)