cp's OEIS Frontend

A221465 Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.

%I A221465 #8 Aug 05 2018 13:46:25
%S A221465 5,88,513,1856,5125,11880,24353,45568,79461,131000,206305,312768,
%T A221465 459173,655816,914625,1249280,1675333,2210328,2873921,3688000,4676805,
%U A221465 5867048,7288033,8971776,10953125,13269880,15962913,19076288,22657381,26757000
%N A221465 Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.
%C A221465 Row 6 of A221463.
%H A221465 R. H. Hardin, <a href="/A221465/b221465.txt">Table of n, a(n) for n = 1..136</a>
%F A221465 Empirical: a(n) = 1*n^5 + 3*n^4 + 1*n^3.
%F A221465 Conjectures from _Colin Barker_, Aug 05 2018: (Start)
%F A221465 G.f.: x*(5 + 58*x + 60*x^2 - 2*x^3 - x^4) / (1 - x)^6.
%F A221465 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>6.
%F A221465 (End)
%e A221465 Some solutions for n=6:
%e A221465 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221465 ..4....1....4....1....2....6....5....3....4....3....6....2....2....4....5....5
%e A221465 ..6....1....2....0....0....5....3....5....6....3....5....6....3....5....4....1
%e A221465 ..5....3....4....0....2....3....4....0....4....2....4....2....1....0....1....6
%e A221465 ..4....1....4....6....6....1....1....0....5....2....1....5....6....5....5....6
%e A221465 ..2....0....3....2....1....3....3....6....0....0....0....1....1....1....2....2
%Y A221465 Cf. A221463.
%K A221465 nonn
%O A221465 1,1
%A A221465 _R. H. Hardin_, Jan 17 2013