OFFSET
1,1
COMMENTS
Table starts
....3.....5.......7........9........11........13.........15..........17
....6....17......36.......65.......106.......161........232.........321
...10....38......99......205.......370.......606........927........1345
...20...125.....476.....1351......3154......6433......11906.......20461
...36...335....1693.....5982.....16790.....39916......84094......161350
...72..1061....7504....34415....119364....341011.....845358.....1878315
..136..3069...29221...169352....713260...2399000....6847916....17247435
..272..9495..123242...904695...4620694..18334295...60473968...173147889
..528.28221..492076..4547008..28033122.130350889..493271080..1595410130
.1056.86149.2021436.23448029.174036890.947356115.4110606460.15000578409
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..313
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
k=2: [order 10]
k=3: [order 29]
Empirical for row n:
n=1: a(n) = 2*n + 1
n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1
n=3: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5); also a cubic polynomial plus a constant quasipolynomial with period 2
n=4: [linear recurrence of order 10; also a quintic polynomial plus a linear quasipolynomial with period 3]
n=5: [order 17; also a quintic polynomial plus a quadratic quasipolynomial with period 12]
EXAMPLE
Some solutions for n=5 k=4
..3....0....3....1....3....3....2....1....2....0....0....1....2....4....0....3
..1....2....1....0....4....2....0....3....1....0....0....0....4....0....2....0
..4....0....0....0....1....4....3....2....2....0....1....0....3....2....2....0
..3....2....2....2....4....2....0....0....1....2....1....4....2....1....4....2
..2....3....3....0....4....4....4....3....2....1....4....1....3....4....1....1
..1....2....1....1....3....4....0....3....3....1....0....3....3....0....2....1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 22 2014
STATUS
approved