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 A225345 T(n,k) = Number of n X k {-1,1}-arrays such that the sum over i=1..n,j=1..k of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute k-across galley oarsmen left-right at n fore-aft positions so that there are no turning moments on the ship). 15
 0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 0, 3, 6, 7, 0, 0, 1, 0, 9, 0, 15, 0, 1, 0, 3, 12, 31, 0, 33, 8, 0, 1, 0, 17, 0, 107, 0, 77, 0, 1, 0, 5, 22, 81, 0, 395, 410, 181, 0, 0, 1, 0, 27, 0, 397, 0, 1525, 0, 443, 0, 1, 0, 5, 34, 171, 0, 2073, 4508, 6095, 0, 1113, 58, 0, 1, 0, 41, 0, 1081, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Table starts .0...1...0.....1....0......1.....0.......1.....0........1......0........1 .0...1...0.....1....0......1.....0.......1.....0........1......0........1 .0...1...0.....3....0......3.....0.......5.....0........5......0........7 .2...3...6.....9...12.....17....22......27....34.......41.....48.......57 .0...7...0....31....0.....81.....0.....171.....0......309......0......509 .0..15...0...107....0....397.....0....1081.....0.....2399......0.....4675 .0..33...0...395....0...2073.....0....7261.....0....19709......0....45385 .8..77.410..1525.4508..11291.25056...50659.95130...168289.283338...457627 .0.181...0..6095....0..63121.....0..364051.....0..1478059......0..4749875 .0.443...0.24893....0.360909.....0.2676331.....0.13280209......0.50435657 LINKS R. H. Hardin, Table of n, a(n) for n = 1..3132 FORMULA Empirical for row n: n=1: a(n) = a(n-2); n=2: a(n) = a(n-2); n=3: a(n) = a(n-2) +a(n-4) -a(n-6); n=4: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5); n=5: a(n) = 3*a(n-2) -2*a(n-4) -2*a(n-6) +3*a(n-8) -a(n-10); n=6: [order 26, even n]; n=7: [order 42, even n]; n=8: [order 28]; n=9: [order 58, even n]; n=10: [order 90, even n]; n=11: [order 102, even n]; n=12: [order 66]. 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 A063074(n/4). Row 3 is A063196(n/2+1). Row 4 is A008810(n+1). Row 5 is A202254(n/2). Sequence in context: A349906 A320439 A321252 * A335427 A083280 A060689 Adjacent sequences:  A225342 A225343 A225344 * A225346 A225347 A225348 KEYWORD nonn,tabl AUTHOR R. H. Hardin May 05 2013 STATUS approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)