OFFSET
1,1
COMMENTS
Table starts
......81......450......1998......7803......28107......95940.....315576
.....450.....2723.....10182.....29737......70590.....148134.....298760
....1998....16625.....77414....247252.....583698....1204422....2363797
....7803....75959....382973...1143174....2351928....4249381....7348144
...28107...305707...1636717...5195288...10966149...19685575...33767784
...95940..1087364...5648005..17656505...36766701...64166071..106040628
..315576..3598487..17980643..54890203..112645903..199063466..333213583
.1011357.11219006..52078415.150904540..295452432..515093745..871426149
.3181653.33417573.140931619.390365827..734787935.1244615026.2111246736
.9876870.95950526.357840627.928677156.1658583509.2727201405.4561812863
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..571
FORMULA
Empirical for column k:
k=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
k=2: [order 42] for n>46
k=3: [order 35] for n>45
k=4: [order 35] for n>47
k=5: [order 26] for n>41
k=6: [same order 26] for n>40
k=7: [same order 26] for n>41
Empirical for row n:
n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
n=2: [order 19] for n>25
n=3: [order 23] for n>30
n=4: [order 19] for n>27
n=5: [same order 19] for n>28
n=6: [same order 19] for n>29
n=7: [same order 19] for n>30
Empirical quasipolynomials for column k:
k=5: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
k=6: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>14
k=7: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
Empirical quasipolynomials for row n:
n=4: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>8
n=5: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>9
n=6: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>10
n=7: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>11
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..0..1....0..0..0..0..1....0..1..1..1..2....0..0..0..1..1
..2..1..0..0..0....2..1..0..0..1....1..0..0..0..1....1..0..0..0..0
..2..1..0..0..1....2..1..1..0..1....2..2..2..2..2....2..2..2..2..2
..2..1..0..0..1....2..2..1..1..1....2..1..1..0..2....1..1..1..1..2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 11 2015
STATUS
approved