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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A199530.
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)
Comments