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A209095 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors. 1

%I #9 Jul 08 2018 10:48:22

%S 5,76,1326,23248,407832,7154944,125526240,2202232576,38635976064,

%T 677829707776,11891846929920,208630607073280,3660216151873536,

%U 64214845877125120,1126585496573239296,19764820171301257216

%N Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

%C Column 3 of A209100.

%H R. H. Hardin, <a href="/A209095/b209095.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) - 44*a(n-2) + 16*a(n-3) for n>4.

%F Conjectures from _Colin Barker_, Jul 08 2018: (Start)

%F G.f.: x*(5 - 4*x)*(1 - 4*x + 2*x^2) / ((1 - 2*x)*(1 - 18*x + 8*x^2)).

%F a(n) = 2^(n-3) + ((9-sqrt(73))^n*(-25+sqrt(73)) + (9+sqrt(73))^n*(25+sqrt(73))) / (16*sqrt(73)) for n>1.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A209100.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 05 2012

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)