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%I #7 Jan 13 2019 08:49:08
%S 17,106,479,1610,4357,10082,20771,39154,68825,114362,181447,276986,
%T 409229,587890,824267,1131362,1524001,2018954,2635055,3393322,4317077,
%U 5432066,6766579,8351570,10220777,12410842,14961431,17915354,21318685
%N Number of length-(4+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
%H R. H. Hardin, <a href="/A268263/b268263.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^5 + n^4 + 4*n^3 + 3*n^2 + 6*n + 2.
%F Conjectures from _Colin Barker_, Jan 13 2019: (Start)
%F G.f.: x*(17 + 4*x + 98*x^2 - 14*x^3 + 17*x^4 - 2*x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=8:
%e ..0....5....4....4....0....4....4....8....5....3....6....6....4....1....0....7
%e ..4....2....3....5....7....1....8....5....1....6....5....7....1....7....4....4
%e ..6....1....0....1....8....7....1....8....4....0....7....8....4....8....3....2
%e ..5....7....5....8....0....0....0....4....0....6....1....5....5....5....8....6
%e ..4....6....0....2....3....0....0....5....0....1....6....6....4....1....0....0
%Y Row 4 of A268261.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 29 2016
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