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Number of (n+1)X4 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or three distinct values, and new values 0..3 introduced in row major order
1

%I #5 Mar 31 2012 12:37:33

%S 995,279526,58464712,11186190570,2073034512148,379491677736164,

%T 69133776440716096,12569987936154929124,2283706683030805890988,

%U 414771759014662924645934,75322194226952483099930400

%N Number of (n+1)X4 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or three distinct values, and new values 0..3 introduced in row major order

%C Column 3 of A210320

%H R. H. Hardin, <a href="/A210315/b210315.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 237*a(n-1) -8494*a(n-2) -300237*a(n-3) +2482313*a(n-4) +58239270*a(n-5) -296444067*a(n-6) -2842201417*a(n-7) +12050668766*a(n-8) +41834205193*a(n-9) -197110345949*a(n-10) -109615007438*a(n-11) +1042214343696*a(n-12) -265321484840*a(n-13) -2283447354472*a(n-14) +1334391576272*a(n-15) +2102283712768*a(n-16) -1614381867264*a(n-17) -554944840192*a(n-18) +578116512768*a(n-19) -98061852672*a(n-20) +1530150912*a(n-21)

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 20 2012