cp's OEIS Frontend

A268069 Number of n X 1 0..3 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.

%I A268069 #9 Feb 26 2018 08:21:57
%S A268069 1,2,4,12,39,138,499,1830,6723,24714,90751,332910,1219947,4466562,
%T A268069 16340935,59746326,218334531,797537226,2912254303,10631252766,
%U A268069 38800597851,141582417426,516549545527,1884336977574,6873201390579
%N A268069 Number of n X 1 0..3 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.
%C A268069 Column 1 of A268073.
%H A268069 R. H. Hardin, <a href="/A268069/b268069.txt">Table of n, a(n) for n = 1..210</a>
%F A268069 Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 30*a(n-3) + 28*a(n-4) + 36*a(n-5) - 36*a(n-6) for n>8.
%F A268069 Empirical g.f.: x*(1 - 4*x - 5*x^2 + 24*x^3 + 11*x^4 - 32*x^5 + 12*x^7) / ((1 - x)*(1 - 3*x)*(1 - 2*x^2)*(1 - 2*x - 6*x^2)). - _Colin Barker_, Feb 26 2018
%e A268069 Some solutions for n=7:
%e A268069 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A268069 ..1....1....0....1....1....1....0....1....1....1....1....1....1....1....0....1
%e A268069 ..2....1....1....2....2....1....1....2....1....0....0....2....2....1....1....2
%e A268069 ..3....0....1....1....0....0....1....3....2....2....1....0....3....2....2....1
%e A268069 ..3....0....0....3....1....0....0....3....1....1....0....0....3....1....3....2
%e A268069 ..1....2....2....3....2....2....0....0....3....1....2....1....0....3....3....0
%e A268069 ..3....3....3....1....2....0....2....2....1....3....1....3....3....0....1....0
%Y A268069 Cf. A268073.
%K A268069 nonn
%O A268069 1,2
%A A268069 _R. H. Hardin_, Jan 25 2016