OFFSET
1,3
COMMENTS
Table starts
....0......0.......0........0........0.........0.........0.........0..........0
....4......7......10.......13.......16........19........22........25.........28
....8.....17......26.......35.......44........53........62........71.........80
...16.....49.....100......169......256.......361.......484.......625........784
...32....139.....342......651.....1068......1593......2226......2967.......3816
...64....393....1210.....2715.....5082......8475.....13056.....18987......26430
..128...1113....4240....11011....22912.....41401.....67936....103975.....150976
..256...3151...14898....45099...105586....210101....374342....615965.....954572
..512...8921...52306...184063...482204...1047967...2006006...3504371....5714456
.1024..25257..183684...752155..2210256...5267759..10894988..20352239...35218688
.2048..71507..645006..3072247.10115926..26387005..58789204.116958723..213700742
.4096.202449.2264978.12550859.46327024.132384353.318224626.675761541.1307528098
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..2080
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) for n>4
k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4)
k=4: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6)
k=5: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6)
k=6: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8)
k=7: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8)
Empirical for row n:
n=2: a(n) = 3*n + 1
n=3: a(n) = 9*n - 1
n=4: a(n) = 9*n^2 + 6*n + 1
n=5: a(n) = 54*n^2 - 69*n + 63 for n>2
n=6: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3
n=7: a(n) = 243*n^3 - 351*n^2 + 237*n + 127 for n>2
EXAMPLE
Some solutions for n=6 k=4
..0....2....3....3....2....2....1....1....2....4....4....2....0....2....4....1
..0....1....4....2....3....3....2....1....3....3....4....2....1....3....3....2
..2....4....4....2....1....0....2....3....4....0....4....1....0....2....4....2
..2....4....1....4....1....0....1....2....0....1....3....4....0....2....4....1
..0....1....1....3....0....2....2....3....1....4....3....3....1....1....0....0
..0....2....1....2....1....3....1....2....2....3....2....3....0....1....0....0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 20 2013
STATUS
approved