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A223056 Number of n X 2 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

%I A223056 #8 Aug 16 2018 16:06:49
%S A223056 2,10,114,1473,19360,255045,3361024,44294253,583749160,7693175205,
%T A223056 101387647984,1336178514333,17609374162360,232072328089365,
%U A223056 3058459941439744,40307163247443213,531204410117077960
%N A223056 Number of n X 2 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.
%C A223056 Column 2 of A223062.
%H A223056 R. H. Hardin, <a href="/A223056/b223056.txt">Table of n, a(n) for n = 1..210</a>
%F A223056 Empirical: a(n) = 18*a(n-1) - 71*a(n-2) + 102*a(n-3) - 48*a(n-4) for n>5.
%F A223056 Empirical g.f.: x*(2 - 26*x + 76*x^2 - 73*x^3 + 16*x^4) / ((1 - x)*(1 - 2*x)*(1 - 15*x + 24*x^2)). - _Colin Barker_, Aug 16 2018
%e A223056 Some solutions for n=3:
%e A223056 ..0..1....0..1....0..1....0..1....0..0....0..1....0..1....0..1....0..1....0..0
%e A223056 ..2..3....2..0....2..2....2..1....1..2....1..0....1..2....2..3....2..3....1..1
%e A223056 ..3..2....0..2....0..3....0..3....2..3....2..0....0..1....3..0....2..1....0..2
%Y A223056 Cf. A223062.
%K A223056 nonn
%O A223056 1,1
%A A223056 _R. H. Hardin_, Mar 13 2013