A250419 T(n,k)=Number of length n+1 0..k arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

3, 5, 6, 7, 17, 10, 9, 36, 38, 20, 11, 65, 99, 125, 36, 13, 106, 205, 476, 335, 72, 15, 161, 370, 1351, 1693, 1061, 136, 17, 232, 606, 3154, 5982, 7504, 3069, 272, 19, 321, 927, 6433, 16790, 34415, 29221, 9495, 528, 21, 430, 1345, 11906, 39916, 119364, 169352

Offset: 1

Author

R. H. Hardin, Nov 22 2014

Keywords

• nonn
• tabl

Comments

Table starts

....3.....5.......7........9........11........13.........15..........17

....6....17......36.......65.......106.......161........232.........321

...10....38......99......205.......370.......606........927........1345

...20...125.....476.....1351......3154......6433......11906.......20461

...36...335....1693.....5982.....16790.....39916......84094......161350

...72..1061....7504....34415....119364....341011.....845358.....1878315

..136..3069...29221...169352....713260...2399000....6847916....17247435

..272..9495..123242...904695...4620694..18334295...60473968...173147889

..528.28221..492076..4547008..28033122.130350889..493271080..1595410130

.1056.86149.2021436.23448029.174036890.947356115.4110606460.15000578409

Examples

			Some solutions for n=5 k=4
..3....0....3....1....3....3....2....1....2....0....0....1....2....4....0....3
..1....2....1....0....4....2....0....3....1....0....0....0....4....0....2....0
..4....0....0....0....1....4....3....2....2....0....1....0....3....2....2....0
..3....2....2....2....4....2....0....0....1....2....1....4....2....1....4....2
..2....3....3....0....4....4....4....3....2....1....4....1....3....4....1....1
..1....2....1....1....3....4....0....3....3....1....0....3....3....0....2....1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..313

Crossrefs

Column 1 is A005418(n+2)

Row 1 is A004273(n+1)

Row 2 is A084990(n+1)

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)

k=2: [order 10]

k=3: [order 29]

Empirical for row n:

n=1: a(n) = 2*n + 1

n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1

n=3: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5); also a cubic polynomial plus a constant quasipolynomial with period 2

n=4: [linear recurrence of order 10; also a quintic polynomial plus a linear quasipolynomial with period 3]

n=5: [order 17; also a quintic polynomial plus a quadratic quasipolynomial with period 12]