A199532 - OEIS

%I #9 May 15 2018 20:43:57

%S 32,320,1324,3734,8470,16682,29750,49284,77124,115340,166232,232330,

%T 316394,421414,550610,707432,895560,1118904,1381604,1688030,2042782,

%U 2450690,2916814,3446444,4045100,4718532,5472720,6313874,7248434,8283070

%N Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two consecutive zero elements.

%C Row 5 of A199530.

%H R. H. Hardin, <a href="/A199532/b199532.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (115/12)*n^4 + (115/6)*n^3 + (41/12)*n^2 - (1/6)*n.

%F Conjectures from _Colin Barker_, May 15 2018: (Start)

%F G.f.: 2*x*(16 + 80*x + 22*x^2 - 3*x^3) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A199530.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2011