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

Author

R. H. Hardin, Nov 14 2014

Keywords

• nonn
• tabl

Examples

			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
		

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: [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