OFFSET
1,1
COMMENTS
Table starts
....2.....3......4.......5........6.........7.........8..........9.........10
....4.....9.....16......25.......36........49........64.........81........100
....8....27.....64.....125......216.......343.......512........729.......1000
...16....79....250.....613.....1276......2371......4054.......6505.......9928
...32...229....964....2969.....7456.....16237.....31844......57649......97984
...64...659...3680...14239....43184....110339....248464.....507935.....962144
..128..1889..13946...67763...248324....745013...1927694....4453031....9406088
..256..5401..52562..320495..1419502...5003189..14883506...38870827...91601150
..512.15419.197288.1508267..8074172..33444515.114432704..338024963..889023812
.1024.43977.738190.7069055.45734140.222678103.876609410.2929722175.8602245520
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9999
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) +a(n-4)
k=3: a(n) = 9*a(n-1) -24*a(n-2) +9*a(n-3) +26*a(n-4) +3*a(n-5)
k=4: a(n) = 16*a(n-1) -93*a(n-2) +220*a(n-3) -112*a(n-4) -192*a(n-5) -2*a(n-6) +8*a(n-7)
k=5: [order 7]
k=6: [order 9]
k=7: [order 9]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 3*n + 1
n=4: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n + 1
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 6*n + 1
n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 15*n^2 + 12*n - 1
n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 28*n^3 + 42*n^2 + 5*n - 1
EXAMPLE
Some solutions for n=6 k=4
..4. .1. .1. .4. .0. .0. .4. .3. .1. .4. .3. .0. .4. .3. .1. .0
..4. .2. .0. .2. .0. .2. .3. .3. .2. .3. .1. .1. .2. .0. .3. .2
..2. .3. .1. .4. .1. .1. .3. .1. .4. .4. .3. .1. .4. .0. .3. .0
..3. .3. .2. .1. .3. .0. .4. .0. .0. .3. .0. .3. .0. .3. .4. .2
..4. .2. .2. .4. .0. .0. .1. .1. .0. .0. .0. .1. .3. .0. .2. .4
..1. .4. .3. .1. .0. .1. .2. .4. .0. .1. .3. .2. .1. .2. .3. .4
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved