OFFSET
1,1
COMMENTS
Table starts
...6...18......48.......96.......174........282.........432.........624
..10...36.....148......380.......862.......1652........2956........4860
..16...72.....460.....1512......4272.......9684.......20236.......37868
..26..144....1436.....6040.....21182......56782......138534......295078
..42..288....4488....24160....105026.....332940......948412.....2299356
..68..576...14040....96736....520788....1952254.....6493036....17917712
.110.1152...43940...387488...2582406...11447368....44452660...139623544
.178.2304..137532..1552448..12805334...67123652...304332258..1088015294
.288.4608..430508..6220480..63497776..393591402..2083523194..8478351478
.466.9216.1347652.24926080.314866606.2307892826.14264241960.66067495706
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9999
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1)
k=3: a(n) = 2*a(n-1) +3*a(n-2) +4*a(n-3) -3*a(n-4) -12*a(n-5) -4*a(n-6)
k=4: a(n) = 3*a(n-1) +5*a(n-2) +2*a(n-3) -16*a(n-4) -28*a(n-5) -8*a(n-6)
k=5: [order 12]
k=6: [order 16]
k=7: [order 22]
Empirical for row n:
n=1: 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=2: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11); also a quartic polynomial plus a linear quasipolynomial with period 12
n=3: [order 27; also a degree 5 polynomial plus a quadratic quasipolynomial with period 840]
n=4: [order 61]
EXAMPLE
Some solutions for n=5 k=4
..3....4....4....0....1....4....3....1....0....0....1....1....1....1....3....4
..4....4....0....1....3....1....2....1....2....3....1....0....3....3....0....1
..4....1....4....1....0....2....3....4....3....1....0....1....4....4....3....1
..3....4....4....0....1....1....3....1....2....0....1....0....0....0....3....4
..0....0....1....4....1....2....2....4....3....1....4....3....0....0....4....1
..3....4....2....0....2....1....3....1....3....4....4....4....3....1....1....4
..3....3....4....0....2....1....2....2....4....2....0....4....1....3....1....4
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 06 2014
STATUS
approved