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Number of n X 1 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.
1

%I #9 Jul 09 2018 10:53:27

%S 3,8,19,35,64,110,185,322,599,1084,1902,3280,5816,10425,18711,33023,

%T 58229,102865,183340,326023,578770,1023268,1814036,3218397,5719285,

%U 10142300,17984603,31872737,56560901,100345791,178058874,315719677

%N Number of n X 1 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.

%C Column 1 of A209374.

%H R. H. Hardin, <a href="/A209367/b209367.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-2) + 4*a(n-4) + 4*a(n-5) + 5*a(n-6) - a(n-7) - 5*a(n-8) - 5*a(n-9) - 5*a(n-10) + a(n-11) + 2*a(n-12) for n>14.

%F Empirical g.f.: x*(3 + 8*x + 16*x^2 + 27*x^3 + 33*x^4 + 31*x^5 - 2*x^6 - 41*x^7 - 54*x^8 - 35*x^9 - 12*x^10 - 11*x^11 - 9*x^12 - 2*x^13) / ((1 - x)*(1 + x - 4*x^4 - 8*x^5 - 13*x^6 - 12*x^7 - 7*x^8 - 2*x^9 + 3*x^10 + 2*x^11)). - _Colin Barker_, Jul 09 2018

%e All solutions for n=5:

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

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

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

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

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

%Y Cf. A209374.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 07 2012