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Number of n X 2 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.
1

%I #8 Jul 12 2018 20:26:44

%S 2,6,57,700,10594,183240,3412100,65953664,1298076552,25767620512,

%T 513555943312,10254450363264,204934235829536,4097247120151424,

%U 81931587030997056,1638507658307430400,32769000295781617792

%N Number of n X 2 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

%C Column 2 of A209744.

%H R. H. Hardin, <a href="/A209738/b209738.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 32*a(n-1) - 258*a(n-2) + 296*a(n-3) + 1256*a(n-4) + 480*a(n-5) for n>6.

%F Empirical g.f.: x*(2 - 58*x + 381*x^2 - 168*x^3 - 1388*x^4 - 536*x^5) / ((1 - 20*x)*(1 - 4*x - 2*x^2)*(1 - 8*x - 12*x^2)). - _Colin Barker_, Jul 12 2018

%e Some solutions for n=5:

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

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

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

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

%e ..1..3....4..1....0..4....0..2....0..1....2..4....2..0....0..1....1..0....3..1

%Y Cf. A209744.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 12 2012