cp's OEIS Frontend

A221543 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221543 #8 Aug 08 2018 07:55:51
%S A221543 3,22,103,303,716,1455,2658,4487,7128,10791,15710,22143,30372,40703,
%T A221543 53466,69015,87728,110007,136278,166991,202620,243663,290642,344103,
%U A221543 404616,472775,549198,634527,729428,834591,950730,1078583,1218912
%N A221543 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221543 Row 5 of A221542.
%H A221543 R. H. Hardin, <a href="/A221543/b221543.txt">Table of n, a(n) for n = 1..210</a>
%F A221543 Empirical: a(n) = 1*n^4 + 1*n^3 - 3*n^2 + 10*n - 9 for n>3.
%F A221543 Conjectures from _Colin Barker_, Aug 08 2018: (Start)
%F A221543 G.f.: x*(3 + 7*x + 23*x^2 - 22*x^3 + 26*x^4 - 18*x^5 + 6*x^6 - x^7) / (1 - x)^5.
%F A221543 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.
%F A221543 (End)
%e A221543 Some solutions for n=6:
%e A221543 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221543 ..0....4....5....4....0....2....3....0....5....0....0....2....0....3....0....6
%e A221543 ..1....0....5....5....1....6....4....0....0....2....0....2....3....4....2....6
%e A221543 ..4....4....1....3....6....2....0....3....2....1....3....3....6....6....0....1
%e A221543 ..6....6....6....1....3....4....0....0....5....3....6....1....3....6....5....6
%Y A221543 Cf. A221542.
%K A221543 nonn
%O A221543 1,1
%A A221543 _R. H. Hardin_, Jan 19 2013