cp's OEIS Frontend

A276300 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.

%I A276300 #9 Feb 05 2019 18:42:35
%S A276300 5,11,45,173,693,2765,11061,44237,176949,707789,2831157,11324621,
%T A276300 45298485,181193933,724775733,2899102925,11596411701,46385646797,
%U A276300 185542587189,742170348749,2968681394997,11874725579981,47498902319925
%N A276300 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.
%H A276300 R. H. Hardin, <a href="/A276300/b276300.txt">Table of n, a(n) for n = 1..210</a>
%F A276300 Empirical: a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) for n>4.
%F A276300 Conjectures from _Colin Barker_, Feb 05 2019: (Start)
%F A276300 G.f.: x*(5 - 9*x - 4*x^2 + 2*x^3) / ((1 - x)*(1 + x)*(1 - 4*x)).
%F A276300 a(n) = (8 + 27*4^n) / 40 for n>1 and even.
%F A276300 a(n) = (72 + 27*4^n) / 40 for n>1 and odd.
%F A276300 (End)
%e A276300 Some solutions for n=4:
%e A276300 ..0..1..2..1. .0..1..0..1. .0..1..0..1. .0..1..0..2. .0..1..2..1
%e A276300 ..0..1..2..0. .0..2..0..1. .2..1..2..1. .0..2..1..2. .0..1..2..0
%e A276300 ..2..1..2..0. .0..2..0..2. .2..1..0..2. .1..2..0..2. .0..1..2..1
%Y A276300 Row 3 of A276299.
%K A276300 nonn
%O A276300 1,1
%A A276300 _R. H. Hardin_, Aug 28 2016