cp's OEIS Frontend

A221464 Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.

%I A221464 #8 Aug 05 2018 13:47:00
%S A221464 3,32,135,384,875,1728,3087,5120,8019,12000,17303,24192,32955,43904,
%T A221464 57375,73728,93347,116640,144039,176000,213003,255552,304175,359424,
%U A221464 421875,492128,570807,658560,756059,864000,983103,1114112,1257795
%N A221464 Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.
%C A221464 Row 5 of A221463.
%H A221464 R. H. Hardin, <a href="/A221464/b221464.txt">Table of n, a(n) for n = 1..137</a>
%F A221464 Empirical: a(n) = 1*n^4 + 2*n^3.
%F A221464 Conjectures from _Colin Barker_, Aug 05 2018: (Start)
%F A221464 G.f.: x*(3 + 17*x + 5*x^2 - x^3) / (1 - x)^5.
%F A221464 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>5.
%F A221464 (End)
%e A221464 Some solutions for n=6:
%e A221464 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221464 ..5....6....3....4....4....1....1....4....5....3....4....4....5....6....5....6
%e A221464 ..0....6....1....5....5....5....3....5....1....3....0....4....5....4....3....0
%e A221464 ..2....5....2....5....5....3....0....3....0....4....0....3....2....0....2....2
%e A221464 ..5....0....1....4....2....0....4....5....6....3....1....2....0....6....0....4
%Y A221464 Cf. A221463.
%K A221464 nonn
%O A221464 1,1
%A A221464 _R. H. Hardin_, Jan 17 2013