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Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..3 introduced in row major order.
2

%I #12 Mar 03 2018 13:57:23

%S 15,110,1024,9894,96288,937926,9140400,89074638,868054608,8459432046,

%T 82439625888,803396884086,7829331882624,76299033606678,

%U 743555689924752,7246159411293342,70615870748013744,688171560086811582

%N Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..3 introduced in row major order.

%C Column 1 of A205352.

%H R. H. Hardin, <a href="/A205347/b205347.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 69*a(n-2) + 248*a(n-3) + 225*a(n-4) - 1296*a(n-5) - 4293*a(n-6) + 1656*a(n-7) + 9072*a(n-8) for n>9.

%F Empirical g.f.: x*(15 + 110*x - 11*x^2 - 1416*x^3 - 5023*x^4 - 4022*x^5 + 19371*x^6 + 26664*x^7 - 3024*x^8) / ((1 - 3*x^2)*(1 - 66*x^2 - 248*x^3 - 423*x^4 + 552*x^5 + 3024*x^6)). - _Colin Barker_, Mar 03 2018

%e Some solutions for n=4:

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

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

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

%e 0 0 1 1 2 3 0 0 0 3 3 1 0 2 1 1 1 0 2 1

%e 3 1 2 1 3 3 0 1 0 0 1 1 1 3 0 2 2 0 1 0

%Y Cf. A205352.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 26 2012