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A206384 Number of n X 3 0..6 arrays with no element equal to another within a city block distance of two, and new values 0..6 introduced in row major order. 1

%I #9 Jun 15 2018 12:45:08

%S 1,4,55,1368,34442,868994,21916090,552801398,13943026782,351682327314,

%T 8870382111250,223735362633678,5643217340398022,142337380859578634,

%U 3590138049351706810,90553101869397071558,2283996915742293943662

%N Number of n X 3 0..6 arrays with no element equal to another within a city block distance of two, and new values 0..6 introduced in row major order.

%C Column 3 of A206389.

%H R. H. Hardin, <a href="/A206384/b206384.txt">Table of n, a(n) for n = 1..150</a>

%F Empirical: a(n) = 21*a(n-1) + 131*a(n-2) - 637*a(n-3) + 486*a(n-4) for n>6.

%F Empirical g.f.: x*(1 - 17*x - 160*x^2 + 326*x^3 + 571*x^4 - 405*x^5) / ((1 - x)*(1 - 20*x - 151*x^2 + 486*x^3)). - _Colin Barker_, Jun 15 2018

%e Some solutions for n=4:

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

%e ..3..4..0....2..3..4....2..3..4....2..3..4....2..3..4....2..3..0....3..4..5

%e ..1..2..5....4..5..6....4..5..6....4..5..0....1..0..5....1..4..5....5..2..1

%e ..6..0..1....3..0..1....3..1..0....3..1..6....4..2..1....6..0..1....1..6..4

%Y Cf. A206389.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 07 2012

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)