A199533 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two consecutive zero elements.

80, 1414, 8342, 30484, 84852, 197962, 407946, 766664, 1341816, 2219054, 3504094, 5324828, 7833436, 11208498, 15657106, 21416976, 28758560, 37987158, 49445030, 63513508, 80615108, 101215642, 125826330, 155005912, 189362760, 229556990

Offset

1,1

Comments

Row 6 of A199530.

Links

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

Formula

Empirical: a(n) = (88/5)*n^5 + 44*n^4 + (58/3)*n^3 - 3*n^2 + (31/15)*n.

Conjectures from Colin Barker, May 15 2018: (Start)

G.f.: 2*x*(40 + 467*x + 529*x^2 + 21*x^3 - x^4) / (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=5:
..1....5...-4....0....5...-3...-1...-3....5....5...-5....0...-3....3....3....4
..3....1....2....5....5...-1....2...-4....4...-3...-2...-3....4....3....1...-1
..3...-5...-3...-3....1...-1....5....1...-5....3....3....4...-3...-1....3....1
.-1....0....4...-2...-3...-4...-3...-2....0....0....5....0...-1...-5....0....0
.-2...-3....4...-4...-3....4...-2....3...-5...-5....2...-3...-1....2...-2...-2
.-4....2...-3....4...-5....5...-1....5....1....0...-3....2....4...-2...-5...-2

Crossrefs

Cf. A199530.

Sequence in context: A038727 A204476 A151603 * A333075 A323962 A296189

Adjacent sequences: A199530 A199531 A199532 * A199534 A199535 A199536

Keyword

nonn

Author

R. H. Hardin, Nov 07 2011

Status

approved