cp's OEIS Frontend

A250354 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.

%I A250354 #7 Nov 13 2018 08:37:46
%S A250354 32,216,888,2724,6900,15186,30072,54888,93924,152550,237336,356172,
%T A250354 518388,734874,1018200,1382736,1844772,2422638,3136824,4010100,
%U A250354 5067636,6337122,7848888,9636024,11734500,14183286,17024472,20303388,24068724
%N A250354 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 A250354 R. H. Hardin, <a href="/A250354/b250354.txt">Table of n, a(n) for n = 1..210</a>
%F A250354 Empirical: a(n) = n^5 + 5*n^4 + 25*n^2 + 5*n for n>2.
%F A250354 Conjectures from _Colin Barker_, Nov 13 2018: (Start)
%F A250354 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 A250354 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 A250354 (End)
%e A250354 Some solutions for n=6:
%e A250354 ..3....1....2....0....3....1....5....1....2....5....6....4....2....6....3....1
%e A250354 ..4....5....1....4....6....1....1....2....2....2....1....1....7....1....1....7
%e A250354 ..2....8....3....7....4....4....2....7....5....6....3....2....5....8....5....2
%e A250354 ..3....8....8....8....8....4....4....7....5....3....8....9....3....5....6....7
%e A250354 .10....6....6....8....9....7....6....6....9....7....5....5....9....5....7....9
%Y A250354 Row 5 of A250351.
%K A250354 nonn
%O A250354 1,1
%A A250354 _R. H. Hardin_, Nov 19 2014