A250355 - OEIS

%I #7 Nov 13 2018 08:37:53

%S 64,622,3349,12734,38543,99344,226247,467642,894599,1606988,2740319,

%T 4473302,7036127,10719464,15884183,22971794,32515607,45152612,

%U 61636079,82848878,109817519,143726912,185935847,237993194,301654823,378901244

%N Number of length 6 arrays x(i), i=1..6 with x(i) in i..i+n and no value appearing more than 2 times.

%H R. H. Hardin, <a href="/A250355/b250355.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 - 5*n^4 + 55*n^3 + 25*n^2 - 61*n + 98 for n>3.

%F Conjectures from _Colin Barker_, Nov 13 2018: (Start)

%F G.f.: x*(64 + 174*x + 339*x^2 + 113*x^3 + 204*x^4 + 168*x^5 - 847*x^6 + 783*x^7 - 336*x^8 + 58*x^9) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

%F (End)

%e Some solutions for n=6:

%e ..1....4....6....5....1....2....1....6....0....3....0....6....2....1....3....5

%e ..1....3....6....2....7....2....5....6....5....5....4....5....3....1....3....1

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

%e ..3....8....5....7....5....7....8....7....4....8....9....3....8....5....5....3

%e ..4....9....4....8....9...10....4...10....6....7...10....9....8....6....5....4

%e ..9...11....7....5...10....9....8....9....6....7....8...10...10....9....9....6

%Y Row 6 of A250351.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2014