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
..15....78....249.....612.....1275......2370......4053.......6504.......9927
..28...222....954....2956.....7440.....16218.....31822......57624......97956
..51...624...3611...14125....43013....110099....248143.....507521.....961625
..92..1740..13544...66925...246798....742487...1923796....4447329....9398090
.164..4824..50442..314935..1407232...4979260..14840928...38800210...91490344
.290.13320.186822.1473779..7982022..33232924.113998742..337209090..887591878
.509.36672.688899.6865098.45074673.220896016.872397577.2920747321.8584628259
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) +a(n-2) -2*a(n-3) -a(n-4)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3)
k=3: a(n) = 12*a(n-1) -51*a(n-2) +81*a(n-3) -3*a(n-4) -63*a(n-5) -24*a(n-6) -9*a(n-7)
k=4: [order 7]
k=5: [order 13]
k=6: [order 15]
k=7: [order 17]
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
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 3*n
n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2
n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 18*n^3 + 36*n^2 - 19*n - 7 for n>2
EXAMPLE
Some solutions for n=6 k=4
..1. .2. .0. .2. .1. .4. .3. .4. .2. .2. .0. .2. .2. .2. .2. .0
..0. .3. .3. .1. .4. .0. .0. .0. .2. .1. .0. .1. .0. .2. .4. .3
..4. .3. .2. .1. .1. .3. .0. .4. .1. .0. .4. .3. .1. .2. .4. .1
..3. .3. .2. .2. .4. .2. .4. .0. .3. .3. .0. .3. .4. .3. .3. .1
..0. .3. .1. .3. .0. .1. .3. .4. .1. .1. .2. .1. .4. .1. .4. .1
..0. .3. .0. .4. .4. .1. .4. .2. .1. .0. .1. .0. .3. .4. .2. .2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved