cp's OEIS Frontend

A268460 Number of length-6 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%I A268460 #12 Jan 14 2019 03:09:36
%S A268460 22,456,3146,13204,41526,108032,245626,504876,959414,1712056,2901642,
%T A268460 4710596,7373206,11184624,16510586,23797852,33585366,46516136,
%U A268460 63349834,84976116,112428662,146899936,189756666,242556044,307062646,385266072
%N A268460 Number of length-6 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
%H A268460 R. H. Hardin, <a href="/A268460/b268460.txt">Table of n, a(n) for n = 1..210</a>
%F A268460 Empirical: a(n) = n^6 + 6*n^5 + 11*n^4 + 2*n^3 + 6*n - 4.
%F A268460 Conjectures from _Colin Barker_, Jan 13 2019: (Start)
%F A268460 G.f.: 2*x*(11 + 151*x + 208*x^2 - 6*x^3 - 13*x^4 + 11*x^5 - 2*x^6) / (1 - x)^7.
%F A268460 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A268460 (End)
%e A268460 Some solutions for n=6:
%e A268460   2  0  2  3  6  4  4  4  3  2  3  6  0  3  1  2
%e A268460   5  2  6  2  3  2  2  2  2  4  1  0  5  2  5  6
%e A268460   2  4  4  6  4  4  5  1  2  4  1  4  4  2  0  0
%e A268460   0  0  0  4  6  1  4  2  4  2  3  0  5  0  3  0
%e A268460   0  4  3  4  1  0  2  4  4  3  6  5  5  0  5  1
%e A268460   6  2  0  5  0  1  2  5  6  4  5  6  1  2  2  2
%Y A268460 Row 6 of A268457.
%K A268460 nonn
%O A268460 1,1
%A A268460 _R. H. Hardin_, Feb 04 2016