A250364 - OEIS

%I #7 Nov 13 2018 12:34:21

%S 64,729,4048,15365,45866,115963,259106,526505,992530,1760831,2971178,

%T 4807021,7503770,11357795,16736146,24086993,33950786,46972135,

%U 63912410,85663061,113259658,147896651,190942850,243957625,308707826,387185423

%N Number of length 6 arrays x(i), i=1..6 with x(i) in i..i+n and no value appearing more than 3 times.

%H R. H. Hardin, <a href="/A250364/b250364.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 5*n^3 + 57*n^2 + 13*n + 1 for n>3.

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

%F G.f.: x*(64 + 281*x + 289*x^2 + 98*x^3 + 44*x^4 + 57*x^5 - 405*x^6 + 482*x^7 - 232*x^8 + 42*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 ..2....1....5....4....5....4....1....0....0....1....5....4....5....5....0....4

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

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

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

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

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

%Y Row 6 of A250361.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2014