A199534 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive zero elements.

200, 6346, 53302, 252154, 860854, 2378412, 5662636, 12071420, 23627580, 43207238, 74751754, 123503206, 196263418, 301676536, 450535152, 656109976, 934503056, 1305024546, 1790593022, 2418159346, 3219154078, 4229958436, 5492398804

Offset

1,1

Comments

Row 7 of A199530.

Links

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

Formula

Empirical: a(n) = (5887/180)*n^6 + (5887/60)*n^5 + (620/9)*n^4 + (11/12)*n^3 + (433/180)*n^2 - (91/30)*n.

Conjectures from Colin Barker, May 16 2018: (Start)

G.f.: 2*x*(100 + 2473*x + 6540*x^2 + 2653*x^3 + 4*x^4 + 4*x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=5:
.-5...-5...-4...-5...-4...-5...-4...-5...-4...-5...-5...-5...-5...-4...-5...-4
..1...-3....1....3....0...-5...-4....4...-4....5...-3....0....5...-4....3....2
..1....4...-1....0....4....2....0...-5...-1....1...-1...-2....3....1...-5....2
.-1...-2....3...-1....5...-2....5....5...-2....3...-1....4...-3....4....1....0
..4...-4...-4....1...-2....5...-1....2....3...-3....5....1....0....4....5...-1
..5....5....3...-2...-1....5...-1....0....3...-5....0....4...-2....1....5....1
.-5....5....2....4...-2....0....5...-1....5....4....5...-2....2...-2...-4....0

Crossrefs

Cf. A199530.

Sequence in context: A220390 A231803 A185988 * A035747 A219414 A022152

Adjacent sequences: A199531 A199532 A199533 * A199535 A199536 A199537

Keyword

nonn

Author

R. H. Hardin, Nov 07 2011

Status

approved