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A268262 Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

%I A268262 #7 Jan 13 2019 08:48:49
%S A268262 9,42,143,378,837,1634,2907,4818,7553,11322,16359,22922,31293,41778,
%T A268262 54707,70434,89337,111818,138303,169242,205109,246402,293643,347378,
%U A268262 408177,476634,553367,639018,734253,839762,956259,1084482,1225193
%N A268262 Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
%H A268262 R. H. Hardin, <a href="/A268262/b268262.txt">Table of n, a(n) for n = 1..210</a>
%F A268262 Empirical: a(n) = n^4 + n^3 + 3*n^2 + 2*n + 2.
%F A268262 Conjectures from _Colin Barker_, Jan 13 2019: (Start)
%F A268262 G.f.: x*(9 - 3*x + 23*x^2 - 7*x^3 + 2*x^4) / (1 - x)^5.
%F A268262 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A268262 (End)
%e A268262 Some solutions for n=8:
%e A268262 ..0....2....4....3....2....2....5....1....7....2....4....8....4....2....4....7
%e A268262 ..2....4....0....6....4....1....0....6....0....8....1....3....2....4....1....6
%e A268262 ..8....6....0....8....0....5....0....4....3....0....6....7....7....0....3....2
%e A268262 ..5....7....2....4....3....1....4....5....1....1....8....0....4....4....8....7
%Y A268262 Row 3 of A268261.
%K A268262 nonn
%O A268262 1,1
%A A268262 _R. H. Hardin_, Jan 29 2016