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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 (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

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)