A251337 - OEIS

%I #8 Nov 29 2018 10:36:57

%S 455,3315,24714,189129,1487375,12022920,99776859,848228679,7364934770,

%T 65097686685,583829921739,5297111776824,48496766872295,

%U 447087492211875,4143325157339274,38549110514055249,359711119457800055

%N Number of (n+1) X (2+1) 0..3 arrays with every 2 X 2 subblock summing to a nonzero multiple of 3.

%H R. H. Hardin, <a href="/A251337/b251337.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*a(n-1) - 252*a(n-2) + 813*a(n-3) + 589*a(n-4) - 5250*a(n-5) - 2310*a(n-6) + 1764*a(n-7).

%F Empirical g.f.: x*(455 - 8970*x + 49869*x^2 - 12684*x^3 - 354270*x^4 - 131964*x^5 + 112896*x^6) / ((1 - 6*x)*(1 - 7*x)*(1 - 6*x - 6*x^2)*(1 - 8*x - 14*x^2 + 7*x^3)). -  _Colin Barker_, Nov 29 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A251343.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014