A199706 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two neighbors equal.

8, 52, 168, 380, 724, 1236, 1940, 2872, 4068, 5552, 7360, 9528, 12080, 15052, 18480, 22388, 26812, 31788, 37340, 43504, 50316, 57800, 65992, 74928, 84632, 95140, 106488, 118700, 131812, 145860, 160868, 176872, 193908, 212000, 231184, 251496

Offset

1,1

Comments

Row 4 of A199704.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6).

Empirical g.f.: 4*x*(2 + 7*x + 9*x^2 + 4*x^3 + 2*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 16 2018

Example

Some solutions for n=5:
..3...-3....3....2....2....2....2...-5...-2...-3....2....0....4...-3....4...-5
..0...-5...-3...-4....1...-1...-1....5...-4....3....0...-2...-4...-2...-3....3
.-3....3...-4...-2...-5....4....0....3....1....5....2...-3...-1....1...-4....4
..0....5....4....4....2...-5...-1...-3....5...-5...-4....5....1....4....3...-2

Crossrefs

Cf. A199704.

Sequence in context: A341626 A215834 A180319 * A302318 A035288 A303012

Adjacent sequences: A199703 A199704 A199705 * A199707 A199708 A199709

Keyword

nonn

Author

R. H. Hardin, Nov 09 2011

Status

approved