A200435 - OEIS

%I #8 May 21 2018 09:22:37

%S 0,1928,50592,473034,2591502,10217182,32233938,86581308,205946004,

%T 445471164,892792604,1680711318,3002811474,5132333154,8444609086,

%U 13443374616,20791260168,31344775440,46194094584,66707951618,94583955318

%N Number of -n..n arrays x(0..7) of 8 elements with zero sum and no two or three adjacent elements summing to zero.

%C Row 5 of A200430.

%H R. H. Hardin, <a href="/A200435/b200435.txt">Table of n, a(n) for n = 1..51</a>

%F Empirical: a(n) = (19328/315)*n^7 - (18373/90)*n^6 + (18602/45)*n^5 - (20887/36)*n^4 + (46687/90)*n^3 - (48359/180)*n^2 + (12499/210)*n.

%F Conjectures from _Colin Barker_, May 21 2018: (Start)

%F G.f.: 2*x^2*(964 + 17584*x + 61141*x^2 + 57919*x^3 + 15963*x^4 + 1053*x^5) / (1 - x)^8.

%F 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>8.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

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

%Y Cf. A200430.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 17 2011