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Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock summing to less than 6.
2

%I #9 Feb 27 2018 10:38:33

%S 150,1740,19269,216912,2430631,27278035,305991368,3432961182,

%T 38513146024,432071200891,4847297854288,54380688812185,

%U 610083824961241,6844384156411424,76785501492801006,861438105302681684

%N Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock summing to less than 6.

%C Column 1 of A184673.

%H R. H. Hardin, <a href="/A184665/b184665.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 10*a(n-1) + 25*a(n-2) - 123*a(n-3) - 73*a(n-4) + 304*a(n-5) + 36*a(n-6) - 144*a(n-7).

%F Empirical g.f.: x*(150 + 240*x - 1881*x^2 - 828*x^3 + 4756*x^4 + 432*x^5 - 2304*x^6) / (1 - 10*x - 25*x^2 + 123*x^3 + 73*x^4 - 304*x^5 - 36*x^6 + 144*x^7). - _Colin Barker_, Feb 27 2018

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A184673.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 19 2011