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A250320
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T(n,k)=Number of length n+2 0..k arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero
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14
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2, 5, 8, 8, 25, 8, 13, 60, 41, 24, 18, 117, 104, 161, 42, 25, 200, 233, 652, 487, 104, 32, 321, 436, 1773, 2432, 1689, 212, 41, 480, 745, 3916, 8767, 12820, 5849, 464, 50, 681, 1152, 7969, 24126, 57833, 61092, 19981, 950, 61, 940, 1733, 14452, 57305, 197848
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OFFSET
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1,1
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COMMENTS
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Table starts
....2......5.......8.......13........18.........25.........32........41
....8.....25......60......117.......200........321........480.......681
....8.....41.....104......233.......436........745.......1152......1733
...24....161.....652.....1773......3916.......7969......14452.....24293
...42....487....2432.....8767.....24126......57305.....119004....228401
..104...1689...12820....57833....197848.....558541....1357424...2953265
..212...5849...61092...363457...1559080....5237161...14866258..37065983
..464..19981..300616..2317841..12424332...50020061..166783380.476368553
..950..67459.1423966.14305925..95711098..461868677.1809575752
.1968.221953.6523576.85334033.709795516.4110975765
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) -6*a(n-3) +3*a(n-4) +3*a(n-5) -2*a(n-6)
Empirical for row n:
n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
n=2: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8); also a cubic polynomial plus a linear quasipolynomial with period 3
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EXAMPLE
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Some solutions for n=5 k=4
..2....2....4....4....0....3....1....4....2....1....4....0....4....4....2....2
..3....3....3....4....2....4....0....3....4....1....2....0....0....4....2....1
..2....0....3....1....0....0....2....0....3....0....2....2....2....3....2....1
..1....4....0....0....1....4....4....1....4....1....0....4....1....4....1....0
..4....1....1....0....3....0....2....0....3....0....2....0....3....0....3....4
..3....2....0....2....4....1....4....1....2....2....3....0....2....2....3....2
..4....3....1....0....2....2....3....4....4....4....1....4....4....0....1....3
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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