A251293 - OEIS

%I #9 Nov 28 2018 08:04:08

%S 84,444,2356,12556,67204,361244,1950036,10570156,57525924,314285244,

%T 1723404916,9483540556,52358197444,289959524444,1610402286996,

%U 8967708907756,50059450561764,280064572814844,1570043088196276

%N Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to 3 6 or 9.

%H R. H. Hardin, <a href="/A251293/b251293.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3).

%F Conjectures from _Colin Barker_, Nov 28 2018: (Start)

%F G.f.: 4*x*(21 - 99*x - 80*x^2) / ((1 - 5*x)*(1 - 5*x - 4*x^2)).

%F a(n) = (1/41)*2^(-n)*(41*10^(1+n) + (123-19*sqrt(41))*(5-sqrt(41))^n + (5+sqrt(41))^n*(123+19*sqrt(41))).

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251300.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014