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A225345 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, 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: A007814 A265330 A272216 * A083280 A060689 A053119

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 October 23 12:10 EDT 2018. Contains 316527 sequences. (Running on oeis4.)