A199902 - OEIS

%I #8 May 17 2018 06:35:05

%S 171,1783,8823,30199,82555,193689,406575,783989,1413739,2414499,

%T 3942247,6197307,9431995,13958869,20159583,28494345,39511979,53860591,

%U 72298839,95707807,125103483,161649841,206672527,261673149,328344171,408584411

%N Number of -n..n arrays x(0..6) of 7 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

%C Row 7 of A199898.

%H R. H. Hardin, <a href="/A199902/b199902.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (151/180)*n^6 + (163/15)*n^5 + (377/9)*n^4 + (395/6)*n^3 + (7429/180)*n^2 + (93/10)*n + 1.

%F Conjectures from _Colin Barker_, May 17 2018: (Start)

%F G.f.: x*(171 + 586*x - 67*x^2 - 104*x^3 + 25*x^4 - 8*x^5 + x^6) / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=6:

%e .-3....0....1....1....3....1....0....3....0....0...-5...-3....0....3....0....4

%e ..4....4...-2....0...-1...-5....0...-4....0....2....3....5...-6....0...-6....0

%e .-2...-2....3...-3....3....1...-5....3...-1....0....0....0....1...-5....4...-3

%e ..5....1....0....5...-6...-3....5...-5....1...-5....6...-6...-6....2...-5....2

%e .-3...-1...-5...-6....4....5...-1....4....0....4...-3....0....6...-1....3...-5

%e ..5....1....5....4...-5...-3....5...-2...-4....0....2....6...-1....5...-2....5

%e .-6...-3...-2...-1....2....4...-4....1....4...-1...-3...-2....6...-4....6...-3

%Y Cf. A199898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011