|
| |
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
