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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.
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 14 2014
STATUS
approved