A222459 - OEIS

%I #8 Mar 15 2018 10:12:31

%S 49,12943,3418807,903055069,238535974201,63007686842527,

%T 16643060295393343,4396153388210813341,1161214600539946100449,

%U 306727092854223318882703,81019916083604999480935207

%N Number of n X 3 0..7 arrays with no entry increasing mod 8 by 7 rightwards or downwards, starting with upper left zero.

%C Column 3 of A222462.

%H R. H. Hardin, <a href="/A222459/b222459.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 270*a(n-1) - 1547*a(n-2).

%F Conjectures from _Colin Barker_, Mar 15 2018: (Start)

%F G.f.: 7*x*(7 - 41*x) / (1 - 270*x + 1547*x^2).

%F a(n) = ((135-sqrt(16678))^n*(-5294+41*sqrt(16678)) + (135+sqrt(16678))^n*(5294+41*sqrt(16678))) / (442*sqrt(16678)).

%F (End)

%e Some solutions for n=3:

%e ..0..0..0....0..0..0....0..0..0....0..0..4....0..0..0....0..0..0....0..0..0

%e ..1..6..3....3..6..3....4..5..2....0..6..0....2..3..4....3..6..1....0..4..6

%e ..2..6..6....6..7..4....5..0..2....6..2..3....7..4..5....5..6..1....4..6..2

%Y Cf. A222462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2013