A268265 - OEIS

%I #8 Jan 13 2019 11:30:28

%S 65,717,5492,29461,118530,384605,1061632,2587557,5717246,11671405,

%T 22326540,40450997,69992122,116419581,187129880,291917125,443515062,

%U 658215437,956567716,1364165205,1912522610,2640050077,3593128752

%N Number of length-(6+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

%H R. H. Hardin, <a href="/A268265/b268265.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + n^6 + 6*n^5 + 5*n^4 + 20*n^3 + 12*n^2 + 20*n + 5 for n>1.

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

%F G.f.: x*(65 + 197*x + 1576*x^2 + 1961*x^3 + 1016*x^4 + 271*x^5 - 76*x^6 + 35*x^7 - 5*x^8) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

%F (End)

%e Some solutions for n=5:

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

%e ..4....3....3....4....3....2....3....0....3....0....4....3....0....3....0....3

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

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

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

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

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

%Y Row 6 of A268261.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 29 2016