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A240637 Number of n X 2 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order. 2

%I #9 Mar 19 2018 13:22:18

%S 1,5,27,193,1391,10072,72941,528283,3826157,27711478,200704271,

%T 1453628917,10528111931,76251331828,552260998337,3999827976463,

%U 28969316843801,209814352850962,1519609968699971,11005988987858473

%N Number of n X 2 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

%C Column 2 of A240642.

%H R. H. Hardin, <a href="/A240637/b240637.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 10*a(n-2) - 6*a(n-3) - 9*a(n-4) for n>6.

%F Empirical g.f.: x*(1 - x - 13*x^2 - 13*x^3 + 2*x^4 + 3*x^5) / ((1 - x)*(1 + x)*(1 - 6*x - 9*x^2)). - _Colin Barker_, Mar 19 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A240642.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 09 2014

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)