cp's OEIS Frontend

A268321 Number of length-(n+1) 0..2 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

%I A268321 #8 Jan 13 2019 11:30:25
%S A268321 2,4,10,25,66,177,485,1348,3797,10812,31076,90015,262432,769199,
%T A268321 2264475,6690450,19825011,58884842,175238730,522316253,1558776782,
%U A268321 4656673837,13922711281,41654206400,124688153137,373402997944,1118614401040
%N A268321 Number of length-(n+1) 0..2 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
%H A268321 R. H. Hardin, <a href="/A268321/b268321.txt">Table of n, a(n) for n = 1..210</a>
%F A268321 Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).
%F A268321 Empirical g.f.: x*(2 - 10*x + 10*x^2 + 11*x^3 - 11*x^4 - 5*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)). - _Colin Barker_, Jan 13 2019
%e A268321 Some solutions for n=10:
%e A268321 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A268321 ..0....0....1....0....0....1....0....1....0....0....0....0....0....1....1....1
%e A268321 ..1....0....0....1....0....0....1....2....1....1....1....1....1....0....0....2
%e A268321 ..2....0....2....1....1....2....1....0....2....1....1....0....2....2....1....1
%e A268321 ..1....0....0....2....1....0....1....0....1....0....0....1....0....0....2....0
%e A268321 ..2....1....0....1....1....1....1....0....1....2....1....1....2....0....0....1
%e A268321 ..1....1....2....1....1....2....1....1....2....2....0....1....1....2....1....0
%e A268321 ..1....0....0....0....1....0....0....2....0....0....0....2....2....1....2....0
%e A268321 ..2....1....0....2....2....2....0....0....0....2....1....2....0....1....1....0
%e A268321 ..1....2....2....1....0....0....2....1....1....0....2....1....0....2....2....2
%e A268321 ..1....1....1....1....0....2....2....0....1....1....0....2....1....0....1....0
%Y A268321 Column 2 of A268327.
%K A268321 nonn
%O A268321 1,1
%A A268321 _R. H. Hardin_, Feb 01 2016