A199836 - OEIS

%I #8 May 16 2018 11:19:41

%S 22,1650,20240,118280,462234,1402934,3579520,8046928,16426926,

%T 31082698,55316976,93593720,151783346,237431502,360051392,531439648,

%U 766015750,1081184994,1497725008,2040195816,2737373450,3622707110,4734799872

%N Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two neighbors summing to zero.

%C Row 5 of A199832.

%H R. H. Hardin, <a href="/A199836/b199836.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (5887/180)*n^6 - (1013/60)*n^5 + (245/36)*n^4 - (35/12)*n^3 + (157/45)*n^2 - (6/5)*n.

%F Conjectures from _Colin Barker_, May 16 2018: (Start)

%F G.f.: 2*x*(11 + 748*x + 4576*x^2 + 5240*x^3 + 1167*x^4 + 32*x^5) / (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=3:

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

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

%e .-1....1....3...-1...-1...-3...-1...-2....1...-1....2....2...-2...-1...-2....1

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

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

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

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

%Y Cf. A199832.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011