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A225310
T(n,k)=Number of nXk -1,1 arrays such that the sum over i=1..n,j=1..k of i*x(i,j) is zero and rows are nondecreasing (ways to put k thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate)
12
0, 1, 0, 0, 1, 2, 1, 0, 3, 2, 0, 3, 6, 7, 0, 1, 0, 9, 16, 15, 0, 0, 3, 12, 31, 0, 35, 8, 1, 0, 17, 52, 113, 0, 87, 14, 0, 5, 22, 83, 0, 443, 474, 217, 0, 1, 0, 27, 122, 427, 0, 1787, 1576, 547, 0, 0, 5, 34, 175, 0, 2341, 5304, 7445, 0, 1417, 70, 1, 0, 41, 238, 1165, 0, 13333, 26498
OFFSET
1,6
COMMENTS
Table starts
..0....1....0......1.....0.......1......0........1......0.........1.......0
..0....1....0......3.....0.......3......0........5......0.........5.......0
..2....3....6......9....12......17.....22.......27.....34........41......48
..2....7...16.....31....52......83....122......175....238.......317.....410
..0...15....0....113.....0.....427......0.....1165......0......2591.......0
..0...35....0....443.....0....2341......0.....8221......0.....22351.......0
..8...87..474...1787..5304...13333..29638....60007.112790....199669..336342
.14..217.1576...7445.26498...77721.197440...449693.939130...1828785.3360554
..0..547....0..31593.....0..461973......0..3437315......0..17085339.......0
..0.1417....0.136351.....0.2791167......0.26700429......0.162204059.......0
LINKS
FORMULA
Empirical for row n:
n=1: a(n) = a(n-2)
n=2: a(n) = a(n-2) +a(n-4) -a(n-6)
n=3: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5)
n=4: a(n) = a(n-1) +a(n-2) -2*a(n-5) +a(n-8) +a(n-9) -a(n-10)
n=5: [order 18]
n=6: [order 42]
n=7: [order 24]
n=8: [order 36]
EXAMPLE
Some solutions for n=4 k=4
..1..1..1..1...-1.-1..1..1...-1.-1.-1..1....1..1..1..1...-1..1..1..1
..1..1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1..1..1
.-1.-1.-1.-1....1..1..1..1...-1..1..1..1....1..1..1..1...-1..1..1..1
.-1.-1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1..1
CROSSREFS
Column 1 is A063865
Column 2 is A007576
Row 3 is A008810(n+1)
Sequence in context: A276276 A157497 A257961 * A131358 A291895 A177351
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin May 05 2013
STATUS
approved