OFFSET
1,16
COMMENTS
Table starts
...0....0......0........0.........1...........5...........15............35
...0....0......0........1........19.........120..........483..........1500
...0....0......1.......33.......413........2859........13976.........54199
...0....1.....33......615......6997.......53950.......315198.......1499394
...1...19....413.....6997.....84910......762227......5385305......31454256
...5..120...2859....53950....762227.....8241540.....71297441.....512868867
..15..483..13976...315198...5385305....71297441....759337545....6725497344
..35.1500..54199..1499394..31454256...512868867...6725497344...73117894428
..70.3923.177848..6083808.157376166..3160111147..50869309436..675539536773
.126.9069.513905.21733215.692347393.17063990547.335549742230.5411459549576
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..449
R. J. Mathar, Counting 2-way monotonic terrace forms over rectangular landscapes, vixra 1511.0225 (2015)
FORMULA
Empirical for column k:
k=1: a(n) = (1/24)*n^4 - (5/12)*n^3 + (35/24)*n^2 - (25/12)*n + 1.
k=2: [polynomial of degree 8]
k=3: [polynomial of degree 12]
k=4: [polynomial of degree 16]
k=5: [polynomial of degree 20]
k=6: [polynomial of degree 24]
k=7: [polynomial of degree 28]
Empirical: with "n+k-3" instead of "n+k-6" T(n,k) = binomial(n+k,k) - 2.
EXAMPLE
Some solutions for n=4, k=4:
..0..1..1..1....0..0..0..0....0..0..0..0....0..1..1..2....0..0..0..1
..1..1..1..1....1..1..1..1....0..0..0..1....1..1..2..2....0..1..1..2
..1..1..2..2....1..1..1..1....1..1..1..1....1..1..2..2....0..1..1..2
..1..2..2..2....1..1..1..2....1..2..2..2....1..2..2..2....1..2..2..2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 24 2014
STATUS
approved