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Number of 2 X (n+1) 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.
2

%I #9 Mar 04 2018 06:41:02

%S 15,85,641,5257,44585,385465,3375401,29817817,264999305,2364834745,

%T 21162573161,189737549977,1703284356425,15303437762425,

%U 137574211418921,1237227532571737,11129405572871945,100130796836040505

%N Number of 2 X (n+1) 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.

%C Row 1 of A206169.

%H R. H. Hardin, <a href="/A206170/b206170.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) - 101*a(n-2) + 192*a(n-3) - 108*a(n-4).

%F Conjectures from _Colin Barker_, Mar 04 2018: (Start)

%F G.f.: x*(15 - 185*x + 626*x^2 - 576*x^3) / ((1 - x)*(1 - 2*x)*(1 - 6*x)*(1 - 9*x)).

%F a(n) = (9 + 3*2^n + 2^(1+n)*3^n + 2*9^n) / 3.

%F (End)

%e Some solutions for n=4:

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

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

%Y Cf. A206169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012