A199899 - OEIS

%I #8 Feb 23 2018 07:28:24

%S 15,49,111,209,351,545,799,1121,1519,2001,2575,3249,4031,4929,5951,

%T 7105,8399,9841,11439,13201,15135,17249,19551,22049,24751,27665,30799,

%U 34161,37759,41601,45695,50049,54671,59569,64751,70225,75999,82081,88479,95201

%N Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

%C Row 4 of A199898.

%H R. H. Hardin, <a href="/A199899/b199899.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (4/3)*n^3 + 6*n^2 + (20/3)*n + 1.

%F Conjectures from _Colin Barker_, Feb 23 2018: (Start)

%F G.f.: x*(3 - x)*(5 - 2*x + x^2) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=6:

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

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

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

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

%Y Cf. A199898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011