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A268256 Number of length-(n+1) 0..3 arrays with new repeated values introduced in sequential order starting with zero.

%I A268256 #8 Jan 11 2019 14:51:33
%S A268256 13,43,143,479,1616,5492,18804,64869,225483,789747,2787100,9910252,
%T A268256 35501416,128109313,465606659,1704022367,6278399432,23282368196,
%U A268256 86873186508,326055377709,1230562324251,4668500002491,17797745988388
%N A268256 Number of length-(n+1) 0..3 arrays with new repeated values introduced in sequential order starting with zero.
%H A268256 R. H. Hardin, <a href="/A268256/b268256.txt">Table of n, a(n) for n = 1..210</a>
%F A268256 Empirical: a(n) = 13*a(n-1) - 60*a(n-2) + 105*a(n-3) - 11*a(n-4) - 94*a(n-5) - 24*a(n-6).
%F A268256 Empirical g.f.: x*(13 - 126*x + 364*x^2 - 165*x^3 - 403*x^4 - 96*x^5) / ((1 - 3*x)*(1 - 4*x)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - _Colin Barker_, Jan 11 2019
%e A268256 Some solutions for n=8:
%e A268256 ..0....0....1....1....0....2....0....1....2....2....0....0....2....2....3....0
%e A268256 ..1....2....2....3....1....3....0....0....0....3....1....3....1....1....0....0
%e A268256 ..3....0....3....0....2....0....0....3....0....1....3....1....0....3....1....0
%e A268256 ..2....2....1....1....3....0....3....0....0....0....2....0....0....2....0....1
%e A268256 ..3....1....0....0....2....1....2....0....1....3....3....3....0....0....3....0
%e A268256 ..2....2....1....0....1....2....1....3....3....1....0....2....1....0....2....0
%e A268256 ..1....3....2....1....3....1....3....1....0....0....0....0....3....2....1....0
%e A268256 ..2....0....1....1....1....0....2....0....3....0....3....0....1....3....0....1
%e A268256 ..0....3....2....3....3....1....0....3....2....3....2....1....2....1....1....2
%Y A268256 Column 3 of A268261.
%K A268256 nonn
%O A268256 1,1
%A A268256 _R. H. Hardin_, Jan 29 2016