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 A275138 Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2. 1

%I #10 Jan 31 2019 19:36:41

%S 4,48,224,1088,5248,25344,122368,590848,2852864,13774848,66510848,

%T 321142784,1550614528,7487029248,36150575104,174550417408,

%U 842803970048,4069417549824,19648886079488,94873214517248,458088402386944

%N Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

%H R. H. Hardin, <a href="/A275138/b275138.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Jan 31 2019: (Start)

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

%F a(n) = 2*((2-2*sqrt(2))^n + (2*(1+sqrt(2)))^n) for n>1.

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 4 of A275142.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 17 2016

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Last modified August 14 22:40 EDT 2024. Contains 375167 sequences. (Running on oeis4.)