A222834 - OEIS

%I #8 Aug 16 2018 08:59:10

%S 7,96,216,600,1536,4056,10584,27744,72600,190104,497664,1302936,

%T 3411096,8930400,23380056,61209816,160249344,419538264,1098365400,

%U 2875557984,7528308504,19709367576,51599794176,135090015000,353670250776

%N Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

%C Column 4 of A222838.

%H R. H. Hardin, <a href="/A222834/b222834.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Aug 16 2018: (Start)

%F G.f.: x*(7 + 82*x + 10*x^2 - 17*x^3) / ((1 + x)*(1 - 3*x + x^2)).

%F a(n) = (3/5)*2^(2-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A222838.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 06 2013