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

1,6

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

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

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

Adjacent sequences: A225307 A225308 A225309 * A225311 A225312 A225313

Keyword

nonn,tabl

Author

R. H. Hardin May 05 2013

Status

approved