A230703 - OEIS

%I #6 Apr 12 2023 08:04:26

%S 30,244,2106,16536,130446,1025430,8053490,63237238,496590056,

%T 3899177780,30617038898,240407287782,1887698838680,14822368917190,

%U 116386479715646,913876264039036,7175832414626878,56345230976142602,442427428831168274

%N Number of (n+3) X (3+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%C Column 3 of A230708.

%H R. H. Hardin, <a href="/A230703/b230703.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +27*a(n-2) -64*a(n-3) -295*a(n-4) -13*a(n-5) +1890*a(n-6) +812*a(n-7) -4466*a(n-8) -467*a(n-9) -3948*a(n-10) +16934*a(n-11) -22529*a(n-12) +17109*a(n-13) -1911*a(n-14) -6225*a(n-15) +731*a(n-16) +3024*a(n-17) -978*a(n-18) -86*a(n-19) +436*a(n-20) -24*a(n-21) -30*a(n-22).

%e Some solutions for n=2

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

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

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

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

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

%Y Cf. A230708.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 28 2013