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

%I

%S 9,42,143,378,837,1634,2907,4818,7553,11322,16359,22922,31293,41778,

%T 54707,70434,89337,111818,138303,169242,205109,246402,293643,347378,

%U 408177,476634,553367,639018,734253,839762,956259,1084482,1225193

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

%H R. H. Hardin, <a href="/A268262/b268262.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + n^3 + 3*n^2 + 2*n + 2.

%F Conjectures from _Colin Barker_, Jan 13 2019: (Start)

%F G.f.: x*(9 - 3*x + 23*x^2 - 7*x^3 + 2*x^4) / (1 - x)^5.

%F 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 (End)

%e Some solutions for n=8:

%e ..0....2....4....3....2....2....5....1....7....2....4....8....4....2....4....7

%e ..2....4....0....6....4....1....0....6....0....8....1....3....2....4....1....6

%e ..8....6....0....8....0....5....0....4....3....0....6....7....7....0....3....2

%e ..5....7....2....4....3....1....4....5....1....1....8....0....4....4....8....7

%Y Row 3 of A268261.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 29 2016

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Last modified December 6 05:22 EST 2022. Contains 358594 sequences. (Running on oeis4.)