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.

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

Author

R. H. Hardin, Dec 02 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..202

Crossrefs

Row 1 is A248434

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]