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A199531 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements. 1

%I

%S 12,72,212,464,860,1432,2212,3232,4524,6120,8052,10352,13052,16184,

%T 19780,23872,28492,33672,39444,45840,52892,60632,69092,78304,88300,

%U 99112,110772,123312,136764,151160,166532,182912,200332,218824,238420,259152

%N Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.

%C Row 4 of A199530.

%H R. H. Hardin, <a href="/A199531/b199531.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n.

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

%F G.f.: 4*x*(3 + 6*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=5:

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

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

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

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

%Y Cf. A199530.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2011

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Last modified September 27 13:48 EDT 2021. Contains 347688 sequences. (Running on oeis4.)