cp's OEIS Frontend

A250363 Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 3 times.

%I A250363 #7 Nov 13 2018 12:48:29
%S A250363 32,243,1016,3094,7712,16700,32608,58826,99704,160672,248360,370718,
%T A250363 537136,758564,1047632,1418770,1888328,2474696,3198424,4082342,
%U A250363 5151680,6434188,7960256,9763034,11878552,14345840,17207048,20507566,24296144
%N A250363 Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 3 times.
%H A250363 R. H. Hardin, <a href="/A250363/b250363.txt">Table of n, a(n) for n = 1..210</a>
%F A250363 Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 5*n^2 + 17*n + 2 for n>2.
%F A250363 Conjectures from _Colin Barker_, Nov 13 2018: (Start)
%F A250363 G.f.: x*(32 + 51*x + 38*x^2 + 3*x^3 + 8*x^4 - 29*x^5 + 22*x^6 - 5*x^7) / (1 - x)^6.
%F A250363 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 A250363 (End)
%e A250363 Some solutions for n=6:
%e A250363 ..1....2....1....2....5....3....5....4....4....3....3....6....2....2....1....3
%e A250363 ..3....2....7....4....6....5....5....3....1....1....5....2....7....5....1....7
%e A250363 ..6....2....6....5....8....2....4....3....5....7....6....5....8....6....3....4
%e A250363 ..4....3....4....8....8....5....6....9....7....4....6....8....4....5....9....9
%e A250363 ..4....7....9....4...10...10...10....9....4...10....4...10....9....4...10...10
%Y A250363 Row 5 of A250361.
%K A250363 nonn
%O A250363 1,1
%A A250363 _R. H. Hardin_, Nov 19 2014