A209369 - OEIS

%I #8 Feb 18 2018 10:02:36

%S 19,84,115,242,690,1922,5460,15488,43792,124002,351154,994050,2814300,

%T 7968032,22558752,63867602,180820962,511936002,1449380900,4103455232,

%U 11617609120,32891508162,93121689570,263644006658,746422898732

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

%C Column 3 of A209374.

%H R. H. Hardin, <a href="/A209369/b209369.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +5*a(n-3) +2*a(n-4) +6*a(n-5) +5*a(n-6) -2*a(n-8) -a(n-9) for n>12.

%F Empirical g.f.: x*(19 + 46*x - 53*x^2 - 83*x^3 - 252*x^4 - 315*x^5 - 423*x^6 - 476*x^7 - 163*x^8 + 111*x^9 + 122*x^10 + 35*x^11) / ((1 - 2*x - 2*x^2 - x^3)*(1 + 2*x^2 + 2*x^4 - x^6)). - _Colin Barker_, Feb 18 2018

%e Some solutions for n=5:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 07 2012