OFFSET
1,1
COMMENTS
Table starts
..2.....3......4.......5........6.........7.........8..........9.........10
..4.....9.....16......25.......36........49........64.........81........100
..6....24.....60.....120......210.......336.......504........720........990
..9....63....222.....570.....1215......2289......3948.......6372.......9765
.12...159....804....2670.....6960.....15477.....30744......56124......95940
.16...394...2872...12380....39560....104006....238224.....492312.....939360
.20...957..10132...56890...223320....695135...1837752....4302612....9168780
.25..2292..35383..259445..1253190...4623815..14121282...37478718...89241015
.30..5419.122480.1175355..6995660..30625210.108123624..325487010..866361210
.36.12678.420752.5293671.38870136.202067047.825227424.2819002698.8390905692
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) -2*a(n-3) +a(n-4)
k=2: a(n) = 6*a(n-1) -9*a(n-2) -8*a(n-3) +24*a(n-4) -16*a(n-6)
k=3: [order 8]
k=4: [order 10]
k=5: [order 12]
k=6: [order 14]
k=7: [order 16]
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 + 2*n
n=4: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n
n=5: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n
n=6: a(n) = n^6 + 6*n^5 + 8*n^4 + (5/3)*n^3 - n^2 + (1/3)*n
n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n
EXAMPLE
Some solutions for n=6 k=4
..3. .2. .1. .0. .1. .3. .1. .0. .0. .1. .0. .2. .4. .3. .0. .4
..3. .0. .0. .3. .3. .4. .4. .2. .3. .4. .4. .4. .2. .4. .4. .4
..1. .3. .1. .0. .3. .4. .2. .4. .1. .1. .0. .2. .0. .2. .2. .2
..0. .4. .4. .3. .0. .0. .1. .0. .2. .4. .2. .4. .2. .4. .1. .4
..2. .0. .0. .2. .3. .0. .2. .4. .3. .2. .0. .0. .4. .1. .1. .2
..1. .0. .1. .4. .4. .4. .3. .4. .4. .3. .2. .0. .0. .3. .2. .4
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 25 2016
STATUS
approved