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A199533 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two consecutive zero elements. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 25 12:28 EST 2021. Contains 341606 sequences. (Running on oeis4.)