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A251428
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
14
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Row 1 is A248434
Sequence in context: A103008 A124742 A152003 * A050855 A031070 A350630
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 02 2014
STATUS
approved