A250229 T(n,k)=Number of length n+1 0..k arrays with the sum of the cubes 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, 208, 223, 64, 8, 67, 132, 473, 704, 651, 128, 9, 88, 187, 872, 1785, 2720, 1907, 256, 10, 113, 248, 1519, 3496, 9437, 10952, 5639, 512, 11, 140, 321, 2392, 6367, 24888, 47953, 45888, 16967, 1024, 12, 171

Offset

1,1

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: [linear recurrence of order 9] for n>12

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

n=3: 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

Table starts
....2.....3......4.......5........6.........7.........8..........9.........10
....4....11.....20......33.......48........67........88........113........140
....8....27.....52......89......132.......187.......248........321........400
...16....79....208.....473......872......1519......2392.......3617.......5184
...32...223....704....1785.....3496......6367.....10640......16909......25152
...64...651...2720....9437....24888.....59415....120412.....222037.....374712
..128..1907..10952...47953...144624....371227....838604....1732385....3243544
..256..5639..45888..264473..1019568...3347259...8983896...21295973...45095084
..512.16967.195516.1440243..6717892..25280899..78435176..215244983..519836920
.1024.52131.852260.8079297.47046932.217539879.789142896.2486304965.6802360404
...
Some solutions for n=6 k=4
..4....2....2....2....3....2....0....2....2....2....1....3....1....2....2....4
..3....1....1....3....0....3....2....1....0....0....4....0....0....4....1....0
..1....0....3....2....2....3....3....4....0....4....1....1....0....3....1....4
..3....3....1....1....0....1....3....1....2....0....3....0....3....3....0....2
..0....1....2....0....0....0....3....3....4....2....2....3....4....2....2....0
..3....4....1....3....3....2....1....4....2....4....0....0....4....2....2....3
..2....2....0....0....3....2....2....2....2....2....1....3....1....0....4....0

Crossrefs

Column 1 is A000079.

Row 2 is A212959.

Sequence in context: A207627 A102539 A240220 * A250277 A250167 A265534

Adjacent sequences: A250226 A250227 A250228 * A250230 A250231 A250232

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2014

Status

approved