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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
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 16 2014
STATUS
approved