OFFSET
1,1
COMMENTS
Table starts
....2.....3.......4........5.........6..........7..........8...........9
....4....11......20.......33........48.........67.........88.........113
....8....37......96......211.......380........639........976........1437
...16...119.....436.....1269......2860.......5831......10460.......17765
...32...373....1880.....7109.....19896......49037.....103556......203615
...64..1151....7836....37881....129648.....380939.....938128.....2121089
..128..3517...32032...195927....810964....2810751....7989940....20567199
..256.10679..129572...996933...4962056...20169871...65768448...191480917
..512.32293..521256..5029417..30034672..142786013..532548628..1748028901
.1024.97391.2091052.25262121.180893724.1004527983.4281269376.15822382297
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..263
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 5*a(n-1) -6*a(n-2)
k=3: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -8*a(n-4)
k=4: [order 8]
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) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a cubic polynomial plus a linear quasipolynomial with period 2
n=4: [order 12; also a quartic polynomial plus a quadratic quasipolynomial with period 12]
n=5: [order 24; also a polynomial of degree 5 plus a cubic quasipolynomialwith period 60]
EXAMPLE
Some solutions for n=5 k=4
..3....0....3....4....0....3....4....4....2....4....4....2....0....4....3....1
..2....0....4....2....0....4....1....4....4....1....3....1....1....2....1....1
..4....4....0....4....4....2....2....2....4....3....4....3....1....2....3....3
..0....2....0....1....2....1....3....2....1....0....3....2....3....1....0....4
..1....2....4....1....3....1....3....3....3....0....0....2....0....4....3....3
..1....0....3....2....0....1....2....4....0....4....0....2....0....2....3....1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved