cp's OEIS Frontend

A221544 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221544 #9 Aug 08 2018 09:07:50
%S A221544 5,54,364,1386,4018,9665,20386,39007,69242,115813,184570,282611,
%T A221544 418402,601897,844658,1159975,1562986,2070797,2702602,3479803,4426130,
%U A221544 5567761,6933442,8554607,10465498,12703285,15308186,18323587,21796162,25775993
%N A221544 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221544 Row 6 of A221542.
%H A221544 R. H. Hardin, <a href="/A221544/b221544.txt">Table of n, a(n) for n = 1..210</a>
%F A221544 Empirical: a(n) = 1*n^5 + 2*n^4 - 6*n^3 + 21*n^2 - 31*n + 23 for n>4.
%F A221544 Conjectures from _Colin Barker_, Aug 08 2018: (Start)
%F A221544 G.f.: x*(5 + 24*x + 115*x^2 - 88*x^3 + 157*x^4 - 153*x^5 + 87*x^6 - 34*x^7 + 8*x^8 - x^9) / (1 - x)^6.
%F A221544 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>10.
%F A221544 (End)
%e A221544 Some solutions for n=6:
%e A221544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221544 ..0....5....0....5....0....2....0....5....0....6....5....3....0....4....2....2
%e A221544 ..5....6....4....1....1....0....3....1....5....6....2....1....4....0....0....1
%e A221544 ..1....4....6....0....6....1....4....6....4....1....2....3....2....6....4....3
%e A221544 ..4....4....3....4....6....4....0....4....4....2....1....6....3....5....6....0
%e A221544 ..2....4....1....1....3....0....4....6....2....0....3....6....5....0....2....6
%Y A221544 Cf. A221542.
%K A221544 nonn
%O A221544 1,1
%A A221544 _R. H. Hardin_, Jan 19 2013