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Number of (n+2)X4 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..3 introduced in row major order
1

%I #5 Mar 31 2012 12:37:02

%S 405,1884,5974,379,1860,2239,8140,32206,107738,407469,1548886,5829163,

%T 22096946,83787824,317534026,1203852903,4564187472,17303757255,

%U 65603491248,248721817370,942974820890,3575088864265,13554191235794

%N Number of (n+2)X4 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..3 introduced in row major order

%C Column 2 of A204642

%H R. H. Hardin, <a href="/A204636/b204636.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +a(n-2) -2*a(n-3) -19*a(n-4) -4*a(n-5) +21*a(n-6) +24*a(n-7) +3*a(n-8) -18*a(n-9) -9*a(n-10) for n>13

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 17 2012