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Number of (n+1)X5 0..2 arrays with the number of equal 2X2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order
1

%I #5 Mar 31 2012 12:37:05

%S 2160,39852,827904,17757552,381376368,8198181984,176201014416,

%T 3787178593416,81398278366368,1749504275073888,37602271807627584,

%U 808189417886692584,17370493977296486352,373345722670556657952

%N Number of (n+1)X5 0..2 arrays with the number of equal 2X2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order

%C Column 4 of A205335

%H R. H. Hardin, <a href="/A205331/b205331.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) +162*a(n-2) -1630*a(n-3) -7292*a(n-4) +40266*a(n-5) +153218*a(n-6) -289954*a(n-7) -912699*a(n-8) +408092*a(n-9) -10757308*a(n-10) -14129504*a(n-11) +156955072*a(n-12) +97653472*a(n-13) -903632160*a(n-14) +1868643200*a(n-15) +1929652736*a(n-16) -19338232320*a(n-17) +24779127808*a(n-18) +69276303360*a(n-19) -225213616128*a(n-20) +28917637120*a(n-21) +670518738944*a(n-22) -903935393792*a(n-23) -187621441536*a(n-24) +744869068800*a(n-25) -53941895168*a(n-26) -180004847616*a(n-27) -335544320*a(n-28) +3154116608*a(n-29) for n>31

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 26 2012