OFFSET
1,2
COMMENTS
Table starts
...1....2......4.......8.......15........26.........42..........64...........93
...2....6.....18......53......142.......339........729........1437.........2638
...4...18.....81.....340.....1238......3891......10761.......26764........60988
...8...53....340....1920.....9075.....36292.....125892......387849......1082111
..15..142...1238....9075....54376....271846....1165921.....4396009.....14863460
..26..339...3891...36292...271846...1679072....8807722....40232545....163307844
..42..729..10761..125892..1165921...8807722...55960651...306796310...1481748658
..64.1437..26764..387849..4396009..40232545..306796310..2001017650..11403395172
..93.2638..60988.1082111.14863460.163307844.1481748658.11403395172..76084625352
.130.4568.129236.2777103.45791493.598768118.6411737114.57777817522.448101581256
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..721
FORMULA
Empirical for column k:
k=1: a(n) = (1/6)*n^3 - (1/2)*n^2 + (4/3)*n
k=2: [polynomial of degree 6]
k=3: [polynomial of degree 9]
k=4: [polynomial of degree 12]
k=5: [polynomial of degree 15]
k=6: [polynomial of degree 18]
k=7: [polynomial of degree 21]
Empirical for "within 1" instead of "within 3" is T(n,k)=binomial(n+k,k)-1
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..1....0..1..2..3....0..0..1..2....0..0..1..1....0..1..2..2
..0..1..1..2....1..2..2..3....1..1..2..2....0..1..1..1....1..1..2..2
..0..1..2..3....2..3..3..4....1..2..2..3....0..1..2..2....1..1..2..2
..1..2..3..4....3..3..3..4....2..2..2..3....1..2..2..3....1..2..2..3
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved