A250277 T(n,k)=Number of length n+1 0..k arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

2, 3, 4, 4, 11, 8, 5, 20, 27, 16, 6, 33, 52, 79, 32, 7, 48, 89, 240, 255, 64, 8, 67, 140, 581, 984, 843, 128, 9, 88, 207, 1132, 2909, 4412, 2763, 256, 10, 113, 288, 1991, 6732, 17885, 20252, 8903, 512, 11, 140, 389, 3156, 14003, 51884, 107387, 91808, 28215, 1024, 12

Offset: 1

Author

R. H. Hardin, Nov 16 2014

Keywords

• nonn
• tabl

Comments

Table starts

....2.....3.......4........5.........6.........7..........8...........9

....4....11......20.......33........48........67.........88.........113

....8....27......52.......89.......140.......207........288.........389

...16....79.....240......581......1132......1991.......3156........4841

...32...255.....984.....2909......6732.....14003......25964.......45303

...64...843....4412....17885.....51884....130335.....281552......564985

..128..2763...20252...107387....381812...1154141....2908232.....6704631

..256..8903...91808...636197...2783500..10172515...30143732....80256473

..512.28215..406748..3664311..19762916..86975297..301550620...925066871

.1024.88195.1759740.20397261.135821156.715749943.2901853512.10244309701

Examples

			Some solutions for n=6 k=4
..4....0....0....1....3....3....4....3....3....1....2....0....4....1....3....3
..2....2....0....1....1....3....2....3....2....4....3....3....4....3....2....4
..4....2....2....4....2....3....0....3....4....4....0....2....4....2....2....4
..2....1....4....4....1....3....4....1....2....1....2....4....2....3....1....2
..2....2....4....2....1....1....4....0....1....2....4....3....1....1....1....4
..2....3....2....1....1....3....2....1....2....1....3....4....2....1....0....0
..4....2....0....3....3....3....0....3....3....1....0....2....4....1....1....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..181

Crossrefs

Column 1 is A000079

Row 2 is A212959

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5) for n>6

k=3: [order 15] for n>18

Empirical for row n:

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

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