cp's OEIS Frontend

A268459 Number of length-5 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%I A268459 #12 Jan 14 2019 03:09:39
%S A268459 16,176,852,2776,7160,15816,31276,56912,97056,157120,243716,364776,
%T A268459 529672,749336,1036380,1405216,1872176,2455632,3176116,4056440,
%U A268459 5121816,6399976,7921292,9718896,11828800,14290016,17144676,20438152,24219176
%N A268459 Number of length-5 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
%H A268459 R. H. Hardin, <a href="/A268459/b268459.txt">Table of n, a(n) for n = 1..210</a>
%F A268459 Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + n^2 + 2*n.
%F A268459 Conjectures from _Colin Barker_, Jan 13 2019: (Start)
%F A268459 G.f.: 4*x*(4 + 20*x + 9*x^2 - 4*x^3 + x^4) / (1 - x)^6.
%F A268459 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 A268459 (End)
%e A268459 Some solutions for n=9:
%e A268459   7  5  8  9  3  4  1  2  0  4  3  1  5  1  5  3
%e A268459   1  4  0  0  3  4  6  4  1  4  6  5  9  8  7  0
%e A268459   3  1  2  5  2  7  1  2  3  7  4  6  7  6  6  3
%e A268459   6  1  7  6  1  6  7  1  6  5  4  8  6  6  5  9
%e A268459   1  1  9  6  5  3  5  8  3  6  4  9  4  6  5  7
%Y A268459 Row 5 of A268457.
%K A268459 nonn
%O A268459 1,1
%A A268459 _R. H. Hardin_, Feb 04 2016