cp's OEIS Frontend

A183356 One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.

%I A183356 #15 Apr 22 2018 04:53:10
%S A183356 36,576,1296,3600,9216,24336,63504,166464,435600,1140624,2985984,
%T A183356 7817616,20466576,53582400,140280336,367258896,961496064,2517229584,
%U A183356 6590192400,17253347904,45169851024,118256205456,309598765056,810540090000
%N A183356 One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.
%C A183356 Column 4 of A183362.
%H A183356 R. H. Hardin, <a href="/A183356/b183356.txt">Table of n, a(n) for n = 1..200</a>
%F A183356 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.
%F A183356 Conjectures from _Colin Barker_, Mar 28 2018: (Start)
%F A183356 G.f.: 36*x*(1 + 14*x + 2*x^2 - 3*x^3) / ((1 + x)*(1 - 3*x + x^2)).
%F A183356 a(n) = (9/5)*2^(3-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.
%F A183356 (End)
%F A183356 Assuming Colin Barker's conjectures, a(n) = (12*Fibonacci(n+1))^2, n>1. - _Ehren Metcalfe_, Apr 21 2018
%e A183356 Some solutions for 5 X 4 with a(1,1)=1:
%e A183356   1 4 3 3    1 1 4 4    1 2 4 1    1 4 2 2    1 1 3 4
%e A183356   2 4 1 1    4 2 3 1    3 2 4 1    1 4 3 3    2 2 3 1
%e A183356   3 3 2 2    4 2 3 1    4 1 3 3    3 2 1 1    3 4 4 2
%e A183356   1 1 4 4    3 1 4 4    4 1 2 2    3 2 4 4    3 1 1 3
%e A183356   4 2 3 1    3 1 2 2    2 3 4 1    1 1 3 2    4 2 2 4
%Y A183356 Cf. A183362.
%K A183356 nonn
%O A183356 1,1
%A A183356 _R. H. Hardin_, Jan 04 2011