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A268257 Number of length-(n+1) 0..4 arrays with new repeated values introduced in sequential order starting with zero.

%I A268257 #8 Jan 13 2019 08:48:39
%S A268257 21,89,378,1610,6877,29461,126591,545627,2359152,10233188,44533546,
%T A268257 194450722,851923695,3745257911,16522347429,73145533817,324971178262,
%U A268257 1448957138290,6483809640888,29119030669064,131250471466965
%N A268257 Number of length-(n+1) 0..4 arrays with new repeated values introduced in sequential order starting with zero.
%H A268257 R. H. Hardin, <a href="/A268257/b268257.txt">Table of n, a(n) for n = 1..210</a>
%F A268257 Empirical: a(n) = 21*a(n-1) - 170*a(n-2) + 634*a(n-3) - 899*a(n-4) - 401*a(n-5) + 1310*a(n-6) + 826*a(n-7) + 120*a(n-8).
%F A268257 Empirical g.f.: x*(21 - 352*x + 2079*x^2 - 4512*x^3 - 220*x^4 + 7524*x^5 + 4261*x^6 + 600*x^7) / ((1 - 4*x)*(1 - 5*x)*(1 - 4*x - x^2)*(1 - 4*x - 2*x^2)*(1 - 4*x - 3*x^2)). - _Colin Barker_, Jan 13 2019
%e A268257 Some solutions for n=7:
%e A268257 ..1....0....2....2....3....0....0....1....1....1....0....2....3....2....1....1
%e A268257 ..0....0....0....3....0....1....4....0....0....2....1....3....0....0....3....3
%e A268257 ..0....3....0....2....2....0....2....3....1....0....0....1....2....3....0....0
%e A268257 ..3....4....3....1....0....0....3....2....0....1....0....3....1....4....2....4
%e A268257 ..4....3....0....3....0....0....2....3....4....3....1....4....0....3....3....0
%e A268257 ..1....2....4....0....0....1....4....0....0....1....4....2....4....0....4....1
%e A268257 ..2....3....1....0....0....0....2....1....4....2....1....0....0....0....1....0
%e A268257 ..4....1....1....0....2....4....3....2....1....4....4....0....2....4....2....1
%Y A268257 Column 4 of A268261.
%K A268257 nonn
%O A268257 1,1
%A A268257 _R. H. Hardin_, Jan 29 2016