cp's OEIS Frontend

A267912 Number of 1 X n 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

%I A267912 #7 Feb 25 2018 08:49:35
%S A267912 1,2,4,11,29,77,201,525,1361,3525,9097,23453,60353,155189,398649,
%T A267912 1023501,2626289,6736677,17274601,44286845,113516321,290925845,
%U A267912 745515417,1910267373,4894426193,12539689989,32125783369,82301320541,210838008449
%N A267912 Number of 1 X n 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%C A267912 Row 1 of A267911.
%H A267912 R. H. Hardin, <a href="/A267912/b267912.txt">Table of n, a(n) for n = 1..210</a>
%F A267912 Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 8*a(n-3) for n>5.
%F A267912 Conjectures from _Colin Barker_, Feb 25 2018: (Start)
%F A267912 G.f.: x*(1 - x - 4*x^2 + 3*x^3 + 4*x^4) / ((1 - 2*x)*(1 - x - 4*x^2)).
%F A267912 a(n) = (1/17)*2^(-5-n)*(-17*4^(1+n) + (85-19*sqrt(17))*(1-sqrt(17))^n + (1+sqrt(17))^n*(85+19*sqrt(17))) for n>2.
%F A267912 (End)
%e A267912 Some solutions for n=8:
%e A267912 ..0..1..1..2..0..1..2..0....0..1..2..0..2..0..1..0....0..1..2..0..0..1..0..2
%Y A267912 Cf. A267911.
%K A267912 nonn
%O A267912 1,2
%A A267912 _R. H. Hardin_, Jan 22 2016