A231435 - OEIS

A231435

Number of (n+2)X(2+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%I #4 Nov 09 2013 06:20:12

%S 2,4,8,17,45,104,280,752,2076,5947,17063,50170,148048,440654,1318362,

%T 3954541,11900191,35855502,108184920,326687124,987055180,2983676881,

%U 9021446161,27283340688,82523932704,249635724500,755206783160

%N Number of (n+2)X(2+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%C Column 2 of A231441

%H R. H. Hardin, <a href="/A231435/b231435.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -24*a(n-3) -4*a(n-4) +70*a(n-5) +7*a(n-6) -29*a(n-7) -24*a(n-8) -202*a(n-9) +21*a(n-10) +269*a(n-11) +185*a(n-12) -177*a(n-13) -123*a(n-14) +5*a(n-15) -116*a(n-16) +144*a(n-17) +30*a(n-18) -36*a(n-19)

%e Some solutions for n=6

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2013