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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079

Row 2 is A212959

Sequence in context: A102539 A240220 A250229 * A250167 A265534 A214554

Adjacent sequences: A250274 A250275 A250276 * A250278 A250279 A250280

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2014

Status

approved