A204374 - OEIS

%I #5 Mar 31 2012 12:37:01

%S 33,51,78,113,182,286,439,710,1128,1775,2873,4628,7422,12063,19589,

%T 31772,51859,84665,138190,226233,370522,606890,995484,1633475,2680738,

%U 4402540,7231998,11881418,19526806,32096793,52763245,86751961,142648787

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

%C Column 1 of A204381

%H R. H. Hardin, <a href="/A204374/b204374.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-4) +2*a(n-5) +3*a(n-6) -6*a(n-7) +3*a(n-8) -a(n-11) +2*a(n-12) -a(n-13) -a(n-14) +2*a(n-15) -a(n-16)

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 14 2012