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A222835 Number of n X 5 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.

%I A222835 #8 Aug 16 2018 08:59:15
%S A222835 19,384,648,1536,4032,9600,22848,55296,133824,322944,779328,1881600,
%T A222835 4542912,10967424,26477376,63922176,154322112,372566400,899454528,
%U A222835 2171475456,5242405824,12656287104,30554979648,73766246400,178087472832
%N A222835 Number of n X 5 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 A222835 Column 5 of A222838.
%H A222835 R. H. Hardin, <a href="/A222835/b222835.txt">Table of n, a(n) for n = 1..210</a>
%F A222835 Empirical: a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) for n>7.
%F A222835 Conjectures from _Colin Barker_, Aug 16 2018: (Start)
%F A222835 G.f.: x*(19 + 346*x - 120*x^2 + 202*x^3 + 173*x^4 - 144*x^5 - 72*x^6) / ((1 + x^2)*(1 - 2*x - x^2)).
%F A222835 a(n) = 48*((-1+i)*((-i)^n+i^(1+n)) + (1-sqrt(2))^n + (1+sqrt(2))^n) for n>3, where i=sqrt(-1).
%F A222835 (End)
%e A222835 Some solutions for n=4:
%e A222835 ..0..1..2..0..1....0..0..1..2..2....0..1..2..3..3....0..0..1..2..0
%e A222835 ..2..1..3..3..1....3..2..1..3..3....0..1..2..0..1....1..2..3..3..0
%e A222835 ..2..0..0..2..2....3..2..0..0..1....2..3..3..0..2....3..2..0..1..1
%e A222835 ..3..3..1..1..0....0..1..3..2..1....2..0..1..1..2....3..1..0..2..2
%Y A222835 Cf. A222838.
%K A222835 nonn
%O A222835 1,1
%A A222835 _R. H. Hardin_, Mar 06 2013