A200431 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two or three adjacent elements summing to zero.

0, 20, 92, 248, 520, 940, 1540, 2352, 3408, 4740, 6380, 8360, 10712, 13468, 16660, 20320, 24480, 29172, 34428, 40280, 46760, 53900, 61732, 70288, 79600, 89700, 100620, 112392, 125048, 138620, 153140, 168640, 185152, 202708, 221340, 241080

Offset

1,2

Comments

Row 1 of A200430.

Links

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

Formula

Empirical: a(n) = (16/3)*n^3 - 6*n^2 + (2/3)*n.

Conjectures from Colin Barker, May 20 2018: (Start)

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

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

(End)

Example

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

Crossrefs

Cf. A200430.

Sequence in context: A225892 A366933 A211140 * A172200 A177291 A169711

Adjacent sequences: A200428 A200429 A200430 * A200432 A200433 A200434

Keyword

nonn

Author

R. H. Hardin, Nov 17 2011

Status

approved