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).

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

Author

R. H. Hardin May 05 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A063865

Column 2 is A007576

Row 3 is A008810(n+1)

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]