A200432 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two or three adjacent elements summing to zero.

0, 80, 520, 1830, 4750, 10250, 19530, 34020, 55380, 85500, 126500, 180730, 250770, 339430, 449750, 585000, 748680, 944520, 1176480, 1448750, 1765750, 2132130, 2552770, 3032780, 3577500, 4192500, 4883580, 5656770, 6518330, 7474750, 8532750

Offset

1,2

Comments

Row 2 of A200430.

Links

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

Formula

Empirical: a(n) = (115/12)*n^4 - (65/6)*n^3 + (65/12)*n^2 - (25/6)*n.

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

G.f.: 10*x^2*(8 + 12*x + 3*x^2) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A200430.

Sequence in context: A085774 A233353 A233354 * A233351 A365887 A107624

Adjacent sequences: A200429 A200430 A200431 * A200433 A200434 A200435

Keyword

nonn

Author

R. H. Hardin, Nov 17 2011

Status

approved