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A268164 Number of n X 1 0..3 arrays with every repeated value in every row and column one larger mod 4 than the previous repeated value, and upper left element zero. 1

%I

%S 1,4,15,55,197,695,2421,8351,28573,97111,328197,1103887,3697709,

%T 12342407,41069973,136292543,451213885,1490644663,4915285029,

%U 16180569199,53184539981,174578141159,572354795445,1874403215135,6132368790877

%N Number of n X 1 0..3 arrays with every repeated value in every row and column one larger mod 4 than the previous repeated value, and upper left element zero.

%H R. H. Hardin, <a href="/A268164/b268164.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 12*a(n-3).

%F Conjectures from _Colin Barker_, Jan 11 2019: (Start)

%F G.f.: x*(1 - x - 3*x^2) / ((1 - 3*x)*(1 - 2*x - 4*x^2)).

%F a(n) = -3^n + (5/8-11/(8*sqrt(5)))*(1-sqrt(5))^n + (1/40)*(1+sqrt(5))^n*(25+11*sqrt(5)).

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Column 1 of A268169.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 27 2016

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Last modified September 19 09:06 EDT 2020. Contains 337178 sequences. (Running on oeis4.)