A250354 - OEIS

%I #7 Nov 13 2018 08:37:46

%S 32,216,888,2724,6900,15186,30072,54888,93924,152550,237336,356172,

%T 518388,734874,1018200,1382736,1844772,2422638,3136824,4010100,

%U 5067636,6337122,7848888,9636024,11734500,14183286,17024472,20303388,24068724

%N Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 2 times.

%H R. H. Hardin, <a href="/A250354/b250354.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 25*n^2 + 5*n for n>2.

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

%F G.f.: 2*x*(16 + 12*x + 36*x^2 - 2*x^3 + 18*x^4 - 33*x^5 + 16*x^6 - 3*x^7) / (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>8.

%F (End)

%e Some solutions for n=6:

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

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

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

%e ..3....8....8....8....8....4....4....7....5....3....8....9....3....5....6....7

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

%Y Row 5 of A250351.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2014