cp's OEIS Frontend

A268461 Number of length-7 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%I A268461 #8 Jan 14 2019 08:40:56
%S A268461 29,1169,11536,62535,240170,736525,1926444,4474451,9476950,18644745,
%T A268461 34530920,60809119,102607266,166901765,262977220,402956715,602407694,
%U A268461 881028481,1263420480,1779951095,2467712410,3371580669,4545381596
%N A268461 Number of length-7 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
%H A268461 R. H. Hardin, <a href="/A268461/b268461.txt">Table of n, a(n) for n = 1..210</a>
%F A268461 Empirical: a(n) = n^7 + 7*n^6 + 16*n^5 + 5*n^4 - 7*n^3 + 18*n^2 - 5*n - 5 for n>1.
%F A268461 Conjectures from _Colin Barker_, Jan 14 2019: (Start)
%F A268461 G.f.: x*(29 + 937*x + 2996*x^2 + 1355*x^3 - 536*x^4 + 335*x^5 - 88*x^6 + 13*x^7 - x^8) / (1 - x)^8.
%F A268461 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.
%F A268461 (End)
%e A268461 Some solutions for n=4:
%e A268461 ..3....2....2....3....3....3....4....2....0....0....3....4....4....4....4....4
%e A268461 ..4....3....2....1....3....0....4....2....3....4....0....0....0....3....2....1
%e A268461 ..2....0....0....1....0....4....4....4....1....3....2....2....2....4....2....3
%e A268461 ..0....3....2....3....3....1....4....2....3....0....3....2....4....2....1....3
%e A268461 ..1....4....2....2....2....0....0....1....3....2....1....4....1....2....3....0
%e A268461 ..3....0....4....1....1....2....2....4....1....0....0....0....3....3....0....2
%e A268461 ..4....0....3....2....2....4....3....0....1....3....0....1....4....3....0....0
%Y A268461 Row 7 of A268457.
%K A268461 nonn
%O A268461 1,1
%A A268461 _R. H. Hardin_, Feb 04 2016