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Number of (2+1)X(n+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
1

%I #6 Nov 22 2013 09:09:33

%S 5,24,139,853,5241,32089,196698,1205422,7387476,45274221,277463582,

%T 1700438900,10421159854,63866201729,391404773682,2398728792093,

%U 14700637816523,90093032996396,552136219923131,3383773364176424

%N Number of (2+1)X(n+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero

%C Row 2 of A232316

%H R. H. Hardin, <a href="/A232318/b232318.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +9*a(n-2) -10*a(n-3) -19*a(n-4) +9*a(n-5) +21*a(n-6) -15*a(n-8) -5*a(n-9) +5*a(n-10) +4*a(n-11) -2*a(n-12) for n>14

%e Some solutions for n=7

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2013