OFFSET
1,7
COMMENTS
Table starts
..0...0.....1......3......6......10.......15........21........28.........36
..0...1.....8.....26.....61.....120......211.......343.......526........771
..1...8....44....153....413.....949.....1948......3676......6497......10894
..3..26...153....615...1953....5281....12686.....27805.....56624.....108549
..6..61...413...1953...7313...23203....64920....164399....383735.....836797
.10.120...949...5281..23203...85801...277585....806347...2142634....5281314
.15.211..1948..12686..64920..277585..1030330...3407823..10237249...28340232
.21.343..3676..27805.164399..806347..3407823..12742873..42993671..132872804
.28.526..6497..56624.383735.2142634.10237249..42993671.161937617..555632319
.36.771.10894.108549.836797.5281314.28340232.132872804.555632319.2105918045
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..2850 (first 479 terms from R. H. Hardin)
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) = (1/2)*n^2 - (3/2)*n + 1
k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 - (13/24)*n^2 - (11/12)*n + 1,
k=3: [polynomial of degree 6]
k=4: [polynomial of degree 8]
k=5: [polynomial of degree 10]
k=6: [polynomial of degree 12]
k=7: [polynomial of degree 14]
Empirical: with "n+k-3" instead of "n+k-4" T(n,k) = binomial(n+k,k) - 2.
EXAMPLE
Some solutions for n=3 k=4
..0..1..1..1....0..0..1..1....0..1..2..3....0..0..1..1....0..0..1..1
..1..1..2..2....0..1..1..2....1..1..2..3....0..0..1..2....0..1..2..2
..1..1..2..3....1..2..2..3....1..2..2..3....1..1..2..3....1..1..2..3
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 24 2014
STATUS
approved