A206164 - OEIS

A206164

Number of (n+1) X 4 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.

%I #8 Jun 13 2018 14:16:01

%S 641,14182,463878,10599630,345652310,7934434238,257597022598,

%T 5939045721006,191982939898678,4445181274166302,143088306500843366,

%U 3326865018494656782,106651001017976490518,2489743322080060401278

%N Number of (n+1) X 4 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 Column 3 of A206169.

%H R. H. Hardin, <a href="/A206164/b206164.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 745*a(n-2) - 489*a(n-3) - 5808*a(n-4) + 1584*a(n-5) + 10368*a(n-6) for n>7.

%F Empirical g.f.: x*(641 + 13541*x - 27849*x^2 - 116389*x^3 + 121496*x^4 + 247632*x^5 - 70272*x^6) / ((1 - x - 4*x^2)*(1 - 741*x^2 - 252*x^3 + 2592*x^4)). - _Colin Barker_, Jun 13 2018

%e Some solutions for n=4:

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

%e ..0..1..0..0....0..1..0..0....0..1..0..1....0..0..0..0....1..1..0..1

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

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

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

%Y Cf. A206169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012