cp's OEIS Frontend

A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

%I A204678 #9 Feb 19 2018 08:54:50
%S A204678 1,2,4,12,40,143,528,1979,7466,28246,106992,405481,1537042,5826959,
%T A204678 22091016,83752328,317527448,1203835147,4564081020,17303737555,
%U A204678 65603438014,248721498050,942974761824,3575088704597,13554190277870
%N A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.
%C A204678 Column 1 of A204685.
%H A204678 R. H. Hardin, <a href="/A204678/b204678.txt">Table of n, a(n) for n = 1..210</a>
%F A204678 Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>6.
%F A204678 Empirical g.f.: x*(1 + x)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - _Colin Barker_, Feb 19 2018
%e A204678 Some solutions for n=5:
%e A204678 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A204678 ..1....1....1....0....1....0....0....1....0....1....0....0....0....1....1....0
%e A204678 ..1....2....0....1....0....1....1....0....1....1....1....1....1....0....0....1
%e A204678 ..0....1....2....0....0....0....0....1....0....0....0....1....0....0....0....0
%e A204678 ..0....0....0....0....1....2....0....0....0....0....0....0....1....1....1....0
%K A204678 nonn
%O A204678 1,2
%A A204678 _R. H. Hardin_, Jan 18 2012