A200433 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two or three adjacent elements summing to zero.

0, 212, 2232, 11008, 36952, 98052, 221984, 448224, 830160, 1437204, 2356904, 3697056, 5587816, 8183812, 11666256, 16245056, 22160928, 29687508, 39133464, 50844608, 65206008, 82644100, 103628800, 128675616, 158347760, 193258260

Offset

1,2

Comments

Row 3 of A200430.

Links

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

Formula

Empirical: a(n) = (88/5)*n^5 - (109/3)*n^4 + 44*n^3 - (107/3)*n^2 + (52/5)*n.

Conjectures from Colin Barker, May 21 2018: (Start)

G.f.: 4*x^2*(53 + 240*x + 199*x^2 + 36*x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A200430.

Sequence in context: A353139 A114880 A348831 * A222950 A356358 A232671

Adjacent sequences: A200430 A200431 A200432 * A200434 A200435 A200436

Keyword

nonn

Author

R. H. Hardin, Nov 17 2011

Status

approved