cp's OEIS Frontend

A222459 Number of n X 3 0..7 arrays with no entry increasing mod 8 by 7 rightwards or downwards, starting with upper left zero.

%I A222459 #8 Mar 15 2018 10:12:31
%S A222459 49,12943,3418807,903055069,238535974201,63007686842527,
%T A222459 16643060295393343,4396153388210813341,1161214600539946100449,
%U A222459 306727092854223318882703,81019916083604999480935207
%N A222459 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 A222459 Column 3 of A222462.
%H A222459 R. H. Hardin, <a href="/A222459/b222459.txt">Table of n, a(n) for n = 1..210</a>
%F A222459 Empirical: a(n) = 270*a(n-1) - 1547*a(n-2).
%F A222459 Conjectures from _Colin Barker_, Mar 15 2018: (Start)
%F A222459 G.f.: 7*x*(7 - 41*x) / (1 - 270*x + 1547*x^2).
%F A222459 a(n) = ((135-sqrt(16678))^n*(-5294+41*sqrt(16678)) + (135+sqrt(16678))^n*(5294+41*sqrt(16678))) / (442*sqrt(16678)).
%F A222459 (End)
%e A222459 Some solutions for n=3:
%e A222459 ..0..0..0....0..0..0....0..0..0....0..0..4....0..0..0....0..0..0....0..0..0
%e A222459 ..1..6..3....3..6..3....4..5..2....0..6..0....2..3..4....3..6..1....0..4..6
%e A222459 ..2..6..6....6..7..4....5..0..2....6..2..3....7..4..5....5..6..1....4..6..2
%Y A222459 Cf. A222462.
%K A222459 nonn
%O A222459 1,1
%A A222459 _R. H. Hardin_, Feb 21 2013