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A251428
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T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero
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14
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2, 9, 12, 16, 41, 12, 29, 116, 97, 40, 42, 237, 380, 341, 56, 61, 432, 1113, 1888, 1003, 144, 80, 725, 2532, 6589, 7458, 3129, 240, 105, 1128, 5097, 18952, 34893, 31980, 9439, 544, 130, 1641, 9120, 44465, 122452, 183341, 127566, 28717, 992, 161, 2316, 15449
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OFFSET
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1,1
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COMMENTS
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Table starts
....2......9......16........29.........42.........61..........80..........105
...12.....41.....116.......237........432........725........1128.........1641
...12.....97.....380......1113.......2532.......5097........9120........15449
...40....341....1888......6589......18952......44465.......94452.......180625
...56...1003....7458.....34893.....122452.....349257......863840......1913597
..144...3129...31980....183341.....791668....2647405.....7658288.....19250197
..240...9439..127566....938895....4868362...19285211....64105154....183394583
..544..28717..520568...4771117...29782800..137949185...526064608...1698285517
..992..86695.2080650..24063611..179832500..976032575..4251906158..15488167451
.2112.261789.8370976.120999825.1084104408.6871688649.34199112972.140282803741
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
k=2: [order 14]
k=3: [order 29]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2
n=2: a(n) = a(n-1) +2*a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) +2*a(n-8) +a(n-10) -a(n-11); also a polynomial of degree 3 plus a quasipolynomial of degree 1 with period 12
n=3: [order 38]
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EXAMPLE
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Some solutions for n=5 k=4
..3....3....1....0....3....1....4....3....3....1....3....1....0....4....0....3
..2....1....4....4....1....0....4....0....0....0....1....0....2....2....1....2
..3....2....1....4....1....0....1....3....1....4....2....3....4....1....3....3
..0....3....0....0....0....4....2....2....3....3....1....1....0....3....1....3
..4....1....3....1....3....3....4....3....3....0....3....3....2....4....3....1
..0....3....4....3....0....1....4....4....0....3....2....4....0....1....1....3
..3....3....0....0....3....1....1....4....0....0....2....4....2....2....4....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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